Mária Lukáčová ist Professorin für Angewandte Mathematik an der Johannes Gutenberg-Universität Mainz. Sie ist RMU Co-Affiliate der TU Darmstadt, stellvertretende Sprecherin des Sonderforschungsbereichs „Multiskalen-Simulationsmethoden für Systeme der weichen Materie“ und Mitglied des Leitungsgremiums  des Profilbereichs „Mainz Institute for Multiscale Modelling (M³ODEL)“. Lukáčová schloss 1994 ihr Studium an der Karls-Universität Prag ab. Anschließend forschte sie als Postdoc an der Universität Magdeburg und habilitierte sich 1998 an der Technischen Universität Brno in Tschechien. Von 2002 bis 2009 war sie Professorin an der Technischen Universität Hamburg und wechselte 2010 nach Mainz. Ihre Forschungsschwerpunkte liegen in der Numerik und Analysis partieller Differentialgleichungen. Sie leistete bedeutende Beiträge zur Entwicklung strukturerhaltender Verfahren für hyperbolische Erhaltungsgleichungen sowie hybrider Multiskalenmethoden für komplexe Fluide. Sie erhielt zahlreiche Auszeichnungen, darunter den Babuška-Preis 1995, den Preis der Tschechischen Akademie der Wissenschaften 2002, die Bronzemedaille der Universität Košice 2013, das Gutenberg Research College Fellowship 2020 sowie die Eduard-Cech-Distinguished-Visitor-Auszeichnung 2026.

Curriculum Vitae, CV cartoon

Arbeitsgruppe

Forschungsinteressen

• Multiscale Problems in Soft Matters
• Hyperbolic Systems of Conservation Laws (truly Multidimensional Methods), see video: Stone in Water, video: Multid Acoustic Wave in Heterogeneous Media (computed by M. Kraft)
• Complex Systems of Conservation Laws with Source Terms;   Multiscale Problems, Asymptotic Preserving and well-balanced Methods
  see video: Perturbation of a Lake at Rest; Video: Solitary Wave running up a Conical Island (computed by M. Dudzinski)
• Numerical Methods for PDE: Finite Volumes / Finite Elements, convergence analysis in multi-D using Young measures
• Uncertainty Quantification Methods
• Geophysical Flows, Atmospherical Flows
• Mathematical and Numerical Modelling of non-Newtonian Fluids: Viscoelastic, Shear-thinning Fluids
  – Application in Hemodynamics: Blood Flow in Elastic Vessels, Fluid-Structure Interaction
• Efficient Solution Strategies for a Flow Solver Based on the Discontinuous Galerkin Methods
• Video: viscoelastic phase separation

• Lectures:
• Video: Viscoelastic phase separation

• Video: Compressible Navier-Stokes equations with potential temperature transport 

• Video: What can we see as a limit of the structure-preserving numerical methods? 

Laufende Projekte

• Focused Programme CoSCaRa: Hyperbolic Balance Laws: Complexity, Scale and Randomness SPP 2410
  supported by DFG, cooperation with M. Herty and C. Helzel
• TRR 146 Multiscale Simulation Methods for Soft Matter Systems;
  Project C3 and Project C5
  supported by DFG, cooperation with B. Dünnweg, P. Virnau
• Gutenberg Research Fellow
• Mainz Institute for Multiscale Modelling (M3odel) 

Abgeschlossene Projekte

• 2020-2023
  Project on Uncertainty quantification by means of neural networks
  supported by Mainz Institut for Multiscale Modelling,  cooperation with  P. Spichtinger (Inst. Atmospheric Physics) and M. Wand (Informatics)
• 2019-2021
  DAAD PPP with Hong-Kong: Efficient data-driven modelling and numerical methods for a class of complex fluids with random coefficients
  supported by DAAD,  cooperation with Zhiwen Zhang (Hong-Kong University)
• 2019-2022
  Sino-German cooperation Project: Advanced Numerical Methods for Nonlinear Hyperbolic
  Balance Laws and Their Applications,
  supported by DFG and Sino-German Center Beijing,  cooperation with G. Warnecke(Magdeburg), S. Jiang, J. Li  (Beijing) et al.

• 2015-2023
  SFB TRR 165 Waves to Weather,
  Project A2, supported by DFG, cooperation with P. Spichtinger

• 2013-2015
  Large time step asymptotic preserving evolution Galerkin methods for multidimensional system of hyperbolic balance laws
  DFG project, cooperation with S. Noelle (RWTH Aachen)

• 2010-2018
  DFG – International Research Training Group  „Mathematical Fluid Dynamics“,
  cooperation with TU Darmstadt

• 2011-2013
  Numerical Study of Chemotaxis and Chemokinekinesis
  Project within the Center for Computation Sciences in Mainz, cooperation with N. Hellmann (biophysics)

• 2011-2013
  Adaptive large time step FVEG methods for multidimensional systems of hyperbolic balance laws
  DFG project, cooperation with S. Noelle (RWTH Aachen)

•  2010-2011
  Adaptive large time step finite volume methods for geophysical flows
  Project within the Center for Computation Sciences in Mainz, cooperation with V. Wirth (meteorology)

• 2010-2012, 2015-2016
  Mathematical modelling and numerical simulation of some non-Newtonian fluids in time-dependent domains
  DFG project

• 2008-2010
  Adaptive semi-implicit FVEG methods for multidimensional systems of hyperbolic balance laws
  DFG project, cooperation with S. Noelle (RWTH Aachen)

• 2006-2008
  Project Based Personell Exchange Programme with Indian Institute of Science, Bangalore, India
  Cooperation with the research group of Professor Ph. Prasad (IISc Bangalore)
  supported by the DAAD

• 2006-2010
  Differential Equations with Applications in Science and Engineering (DEASE) http://www.wpi.ac.at/DEASE/, Marie Curie Actions, EU-HRM
  Partners: Wolfgang Pauli Institute Wien, Uni-Hamburg, ENS Paris, MPI Toulouse, FORTH Heraklion

• 2002-2005
  DFG-Graduiertenkolleg (Uni-Hamburg, TUHH) Erhaltungsprinzipien in der Modellierung und Simulation mariner, atmosphärischer und technischer Systeme

• 2002-2005
  Hyperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis (HYKE)
  EU-Research Training Network

• 2001-2003
  Grant of the VolkswagenStiftung Agency „Numerical modelling of complex compressible flows with genuinely multi-dimensional methods“
  Project in the Programme: „Cooperation with Scientists and Engineers from the Central and Eastern Europe“, Technical University Brno
  (cooperation with G. Warnecke)

• 1999-2002
  Grant of the Czech Grant Agency: „Mathematical modelling of some engineering problems in continuum mechanics“, Technical University Brno
  (cooperation with A. Zenisek and J. Francu)

• 1999-2002
  Grant of the Technical University of Brno CZ 39001/220
  (cooperation with M. Jicha and A. Zenisek)

• 1997-1999
  Grant of the Czech Grant Agency: „Mathematical modelling of some nonlinear problems of continuum mechanics“, Technical University Brno
  (cooperation with A. Zenisek and J. Francu)

• 1996-2000
  DFG-Project: „Genuinely multi-dimensional methods for hyperbolic conservation laws“, University of Magdeburg
  (cooperation with G. Warnecke and K.W. Morton), see photo

• 1993-1994
  Grant of the Czech Grant Agency, Charles University Prague
  (cooperation with M. Feistauer and J. Felcman)

Books

• E. Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She:  Numerical Analysis of Compressible Fluid Flows,     MS&A. Modeling, Simulation and Applications, 20. Springer, 2021.

Journals

• [142] M. Lukacova-Medvid’ova, B. She. Lax convergence theorems and error estimates of a finite element method for the incompressible Euler system, arXiv 2604.00783, 2026
• [141] E. Feireisl, M. Lukacova-Medvid’ova, B. She and Y. Yuan. Temperature-driven turbulence in compressible fluid flows, arXiv 2603.28158, 2026
• [140] E. Feireisl, M. Lukacova-Medvid’ova, B. She and Y. Yuan. Convergence of a finite volume method to weak solutions for the compressible Navier-Stokes-Fourier system, arXiv2603.20758, 2026
• [139] S. Chu, M. Herty, M. Lukacova-Medvid’ova, and Y. Zhou. Solving random hyperbolic conservation laws using linear programming, SIAM J. Sci. Comput., 2025
• [138] M. Lukacova-Medvidova,  F. Thein, G. Warnecke, Y. Yuan: A note on relations between convexity and concavity of thermodynamic functions, arXiv Preprint arXiv:2510.24440, 2025.
• [137] M. Dumbser, M. Lukacova-Medvidova, A. Thomann: Convergence of a Hyperbolic Thermodynamically Compatible finite volume scheme for the Euler equation, Num. Math. 2025.
• [136] A. Chertock, M. Herty, A. Ishakov,  A. Ishakova, A. Kurganov,  M. Lukacova-Medvidova:  Numerical study of random Kelvin-Helmholtz instability, accepted to Comm. Comp. Phys. 2026.
• [135]  E. Feireisl, A. Jüngel, M. Lukacova-Medvidova: Maximal dissipation and well-posedness of the Euler system of gas dynamics, arXiv Preprint arXiv:2501.05134, 2025.
• [134] E. Feireisl,  M. Lukacova-Medvidova, C. Yu: Oscillatory approximations and maximum entropy principle for the Euler system of gas dynamics, arxiv Preprint, 2025
• [133] M. Lukacova-Medvidova, S. Schneider: Random compressible Euler flows, Proceeding HYP 2024, 2025.
• [132]  M. Lukacova-Medvidova, Z. Tang, Y. Yuan: Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems, arXiv Preprint 2511.00957, accepted to Comm. Comp. Phys. 2025.
• [131]  E. Feireisl, , M. Lukacova-Medvidova,  H. Mizerova, C. Yu; Monte Carlo method and the random isentropic Euler system, accepted Stoch. Partial Diff. Eqs Comp, Springer, 2026.
• [130]  M. Lukacova-Medvidova,  S. Schneider: Estimatable variation neural networks and their application to ODEs and scalar hyperbolic conservation laws, ArXiv Preprint arXiv:2409.08909, 2024.
• [129] A. Brunk, H. Egger, O. Habrich, M. Lukáčová-Medvid’ová: Error analysis for a second-order approximation of a viscoelastic phase separation model, Num. Math. 2025
• [128] A. Brunk, J. Giesselmann, M. Lukáčová-Medvid’ová: A posteriori error control for the Allan-Cahn equation with variable mobility, SIAM J. Num. Anal. 2025.
• [127] D. Kuzmin, M. Lukáčová – Medvid’ová, P. Öffner: Consistency and convergence of flux-corrected finite element method for nonlinear hyperbolic problems, J. Num. Math. 2025.
• [126] M. Lukáčová – Medvid’ová, B. She, Y. Yuan: What is the limit of structure-preserving numerical methods for compressible flows? Numerical mathematics and advanced applications—ENUMATH 2023. Vol. 1, 17–33, Lect. Notes Comput. Sci. Eng., 153, Springer, Cham, 2025.
• [125]  M. Lukáčová-Medvid’ová, B. She, B., Y. Yuan: Convergence analysis for the Monte-Carlo method for the random Navier-Stokes-Fourier system,  SIAM J. Num. Anal.  63(3), 2025, 1254-1280.
• [124]  M. Lukáčová-Medvid’ová, B. She, B., Y. Yuan:  Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system,  IMA J. Num. Anal. 45 (2), 2025,  1054–1101,
• [123] M. Lukáčová-Medvid’ová, A. Schömer: Conditional regularity of the compressible Navier-Stokes equations with potential temperature transport, J. Diff. Eqs.  423, l 2025, 1-40.
• [122]  M. Lukáčová-Medvid’ová, B. She,  & Y. Yuan:  Penalty method for the Navier–Stokes–Fourier system with Dirichlet boundary conditions: convergence and error estimates.Numer. Math. 157, 2025, 1079–1132.
• [121] E. Feireisl, M. Lukáčová-Medvid’ová, B. She, B., Y. Yuan: Error analysis of the Monte Carlo method for compressible magnetohydrodynamics, Math. Models and Meth. Appl. Sci. 35(9), 2025, 2047-2097.
• [120] M. Anandan, M. Lukáčová-Medvid’ová, S.V. R. Rao:  An asymptotic preserving scheme satisfying entropy stability or the barotropic Euler system  SeMA 1-29,  2025.
• [119] E. Feireisl, M. Lukáčová-Medvid’ová, B. She, B., Y. Yuan: Convergence of Numerical Methods for the Navier–Stokes–Fourier System Driven by Uncertain Initial/Boundary Data.Found Comput Math, 2024.
• [118] M. Lukáčová-Medvid’ová, C. Rohde: Mathematical Challenges for the Theory of Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness.Jahresber. Dtsch. Math. Ver. 2024
• [117] A. Chertock, M. Herty,  A. Ishakov, S. Janajra, A. Kurganov, M. Lukacova-Medvidova: New high-order numerical methods for hyperbolic systems of nonlinear PDEs with uncertainties, Comm. Appl. Math. Comp. 6(3), 2024, 2011–2044.
• [116] E. Chudzik, C. Helzel, M. Lukacova-Medvidova: Active Flux methods for hyperbolic systems using the methods of bicharacteristics, J. Sci. Comp. 99(16), 2024
• [115] M. Lukacova-Medvidova, I. Peshkov, A. Thomann. An implicit-explicit solver for a two-fluid single-temperature model, J. Comput. Phys. 498, 2024, 112696
• [114] M. Lukacova-Medvidova, Y. Yuan. Convergence of a generalized Riemann problem scheme for the Burgers equation,  Comm. Appl. Math. Comput. 6, 2024, 2215–2238
• [113]  M. Lukacova-Medvidova, G. Puppo, A. Thomann. An all Mach number finite volume method for isentropic two-phase flow, J. Numer. Math. 31(3), 2023, 175-204.
• [112] A. Brunk, H. Egger, O. Habrich, and M. Lukacova-Medvidova: A second-order fully-balanced structure-preserving variational discretization scheme for the Cahn-Hilliard Navier-Stokes system, Math. Mod. Meth. Appl. Sci. 12(33) (2023)
• [111]  T. Janjic, M. Lukacova-Medvidova,  Y. Ruckstuhl, B. Wiebe: Comparison of uncertainty quantification methods for cloud simulation, Quarterly Journal of the Royal Meteorological Society, (2023)  http://doi.org/10.1002/qj.4537
• [110] E. Feireisl, M. Lukacova-Medvidova:Convergence of a stochastic collocation finite volume method for the compressible Navier–Stokes system, Ann. Appl. Probab., 2023
• [109] E. Feireisl, M. Lukacova-Medvidova: Statistical solutions for the Navier-Stokes-Fourier system, Stoch PDE: Anal Comp. 2023
• [108] M. Lukacova-Medvidova, Y. Yuan: Convergence of first-order finite volume method based on exact Riemann solver for the complete compressible Euler equations, Num. Methods PDE 1-34 (2023)
• [107] D. Basaric, M. Lukacova-Medvidova, H. Mizerova, B. She, Y. Yuan: Error estimates of a finite volume method for the compressible Navier–Stokes–Fourier system, Math. Comp. (2023)
• [106] A. Brunk, H. Egger, O. Habrich, M. Lukacova-Medvidova: Stability and discretization error analysis for the Cahn-Hilliard system via relative energy estimates, ESIAM M2AN (2023)
• [105] A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, B. Wiebe: Stochastic Galerkin method for cloud simulations, Part II: A fully random Navier-Stokes-cloud model, J. Comput. Phys. (2023)
• [104] E.Feireisl, M. Lukacova-Medvidova, B. She: Improved error estimates for the finite volume and the MAC schemes for the compressible Navier-Stokes system, Numer. Math. (2023)
• [103] R. Abgrall, M. Lukacova-Medvidova, P.Öffner: Convergence of residual distribution schemes for compressible Euler equations via dissipative weak solutions, Math. Mod. Meth. Appl. Sci., (2023)
• [102] M. Lukacova-Medvidova, P.Öffner: Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions, Appl. Math. Comput. 436 (2023)
• [101] E. Feireisl, M. Lukacova-Medvidova, B. She, Y. Yuan: Convergence and error estimates for compressible fluid flows with random data: Monte Carlo method, Math. Mod. Meth. Appl. Sci., Vol. 32, No. 14 (2022) 2887-2925, (2022)
• [100] A. Cherock,  S. Chu, A. Kurganov, M. Herty, M. Lukacova-Medvidova,  Local characteristic decomposition based central-upwind scheme., J. Comput. Phys. 473 (2023)
• [99] A. Brunk, M. Lukacova-Medvidova: Relative energy and weak-strong uniqueness of a two-phase viscoelastic phase separation model, ZAMM,  (2022).
• [98] A. Chertock, P. Degond, G. Dimarco,  M. Lukacova-Medvidova, A. Ruhi: On a hybrid continuum-kinetic model for complex fluids, J. Part. Diff. Eq. Appl.,  (2022).
• [97] D. Basaric, E. Feireisl, M. Lukacova-Medvidova, H. Mizerova, Y. Yuan: Penalization method for the Navier-Stokes-Fourier system, ESAIM: M2AN (2022), DOI: https://doi.org/10.1051/m2an/2022063
• [96] M. Lukacova-Medvidova, A. Schömer: Compressible Navier-Stokes equations with potential
  temperature transport: stability of the strong solution and numerical error estimates, J. Math. Fluid Mech. 25, Paper No. 1, 38 pp., (2023).
• [95] M. Lukacova-Medvidova, A. Schömer: Existence of dissipative solutions to the compressible Navier-Stokes system with potential temperature transport. J. Math. Fluid Mech. 24(3) (2022),  Paper No. 82.
• [94] N. Kolbe, L. Hexemer, L.-M. Bammert, A. Loewer, M. Lukacova-Medvidova, S. Legewie. Data-based stochastic modeling reveals sources of activity bursts in single-cell TGF-β signaling, , PLoS Computational Biology 18(6): e1010266, (2022).
• [93] E. Feireisl, M. Lukacova-Medvidova, S. Schneider, B. She:  Approximating viscosity solutions of the Euler system. Math. Comp. 91(337)  (2022), 2129–2164.
• [92] M. Lukacova-Medvidova, B. She, Y. Yuan: Error estimate of the Godunov method for multidimensional compressible Euler equations, J. Sci. Comput. 91:71 (2022) 
• [91] A. Kurganov, Y. Liu,  M. Lukacova-Medvidova: A well-balanced asymptotic preserving scheme for the two-dimensional rotating shallow water equations with nonflat bottom topography.  SIAM J. Sci. Comput. 44 (3), (2002), A1655–A1680.
• [90] M. Lukacova-Medvidova, B. She, Y. Yuan: Error estimate of the Godunov method for multidimensional compressible Euler equations, J. Sci. Comput. 91:71 (2022) 
• [89]  A. Brunk,  M. Lukacova-Medvidova: Global existence of weak solutions to viscoelastic phase separation: Part II Degenerate Case, Nonlinearity 35 (2022),  3459–3486
• [88]  A. Brunk,  M. Lukacova-Medvidova: Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case,  Nonlinearity 35 (2022), 3417–3458.
• [87]  A. Brunk, Y. Lu, M. Lukacova-Medvidova: Existence, regularity  and weak-strong  uniqueness for three dimensional Peterlin viscoelastic model, Commun. Math. Sci. 20(1) (2022),  201–230.
• [86] F. Tedeschi, G. Giusteri, L. Yelash, M. Lukacova-Medvidova:  A multi-scale method for complex flows of non-Newtonian fluids, Mathematics in Engineering 4(6),  (2022),  1-22.
• [85] D. Spiller, A. Brunk, O. Habrich, H. Egger, M. Lukáčová-Medvid’ová, B. Dünweg: Systematic derivation of hydrodynamic equations for viscoelastic phase separation, J. Phys.: Condens. Matter 33 364001 (2021).
• [84] R. Datta,  L. Yelash, F. Schmid, F. Kummer, M. Oberlack, M. Lukacova-Medvidova, P. Virnau: Shear-thinning in oligomer melts-molecular origin and applications, Polymers 2021, 13, 2806.
• [83] V. Kucera, M. Lukacova-Medvidova,  S. Noelle, J. Schütz: Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations,  Num. Math 150, 79-103 (2022)
• [82] A. Brunk, B. Duennweg, H. Egger, O.  Habrich, M. Lukacova-Medvidova,  D. Spiller: Analysis of a viscoelastic phase separation model, J. Phys.: Condens. Matter (2021)
• [81] E.Feireisl, M. Lukacova-Medvidova, B. She, Y. Wang: Computing oscillatory solutions of the Euler system via K-convergence, M3AS Math. Mod. & Methods Appl. Sci. (2021) DOI:10.1142/S0218202521500123
• [80] E.Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She: On the convergence of a finite volume method for the Navier–Stokes–Fourier system, IMA J. Num. Anal. (2020) DOI: 10.1093/imanum/draa060
• [79]  E.Feireisl, M. Lukacova-Medvidova, H. Mizerova: K-convergence as a new tool in numerical analysis, IMA J. Num. Anal. 40 (2020), 2227–2255  DOI: 10.1093/imanum/drz045
• [78] Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She: Convergence of a finite volume scheme for the compressible Navier-Stokes system,  ESAIM: Math.  Model. Num. 53 (2019) 1957–1979.
• [77] J.A. Carrillo, N. Kolbe, M. Lukacova-Medvidova: A hybrid mass transport finite element method for Keller–Segel type systems,  J. Sci. Comp., 80, (2019), 1777-1804.
• [76] J. Zeifang, J. Schütz, K. Kaiser, A. Beck, M. Lukacova-Medvidova, S. Noelle: A novel full-Euler low Mach number IMEX splitting,  CiCP 27 (2020), 292-320.
• [75] A. Chertock, A. Kurganov, M. Lukacova-Medvidova, P. Spichtinger, B. Wiebe: Stochastic Galerkin method for cloud simulation, Math. Clim. Weather Forecast.  5 (2019), 65-106, DOI: 10.1515/mcwf-2019-0005
• [74]  P. Strasser, G. Tierra, B. Dünweg, M. Lukacova-Medvidova: Energy-stable linear numerical schemes for polymer-solvent phase field models, Comp. Math. Appl. 77(1),  (2019), 125-143.
• [73]  P. Gwiazda, M. Lukacova-Medvid’ova, H. Mizerova, A. Szwierczewska-Gwiazda:  Existence of global weak solutions to the kinetic Peterlin model, Nonlinear Analysis: Real World App. 44, (2018), 465-478, DOI: 10.1016/j.nonrwa.2018.05.016
• [72] E. Feireisl, M. Lukacova-Medvidova, H. Mizerova: A finite volume scheme for the Euler system inspired by the two velocities approach, Num. Math.  144, (2020), 89-132, DOI: 10.1007/s00211-019-01078-y
• [71] A. Chertock, A. Kurganov, M. Lukacova-Medvidova, S. Nur Oezcan: An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions, Kinetic and Related Models 12(1), (2019),195–216.
• [70] J. Giesselmann , N. Kolbe, M. Lukacova-Medvidova,  N. Sfakianakis: Existence and uniqueness of global classical solutions to a two species cancer invasion haptotaxis model,  Disc. Cont. Dyn.Systems-B 23(10) (2018), 4391-4431. DOI: 10.3934/dcdsb.2018169
• [69] E. Feireisl,  M. Lukáčová-Medvid’ová, H. Mizerová: Convergence of finite volume schemes for the Euler equations via dissipative measure–valued solutions, Found Comput Math 20 (2020). 923-966. DOI: 10.1007/s10208-019-09433-z
• [68] A. Chertock, M. Dudzinski, A. Kurganov, M. Lukacova-Medvidova: Well-Balanced schemes for the shallow water equations with Coriolis forces, Num. Math. 138 (2018), 939–973 DOI: 10.1007/s00211-017-0928-0 
• [67] S. Stalter, L. Yelash, N. Emamy, A. Statt, M. Hanke, M. Lukacova-Medvidova, P. Virnau: Molecular dynamics simulations in hybrid particle-continuum schemes: Pitfalls and caveats , Comput. Phys. Commun. 224 (2018), 198–208. DOI: 10.1016/j.cpc.2017.10.016
• [66] M. Lukacova-Medvidova, B. Dünweg, P. Strasser, N. Tretyakov: Energy-stable numerical schemes for multiscale simulations of polymer-solvent mixtures, in Mathematical Analysis of Continuum Mechanics and Industrial Applications II, (Eds. Patrick van Meurs et al.), Springer (2018)
• [65] E. Feireisl, M. Lukacova-Medvidova: Convergence of a mixed finite element finite volume scheme for the isentropic Navier-Stokes system via dissipative measure-valued solutions, arXiv Found. Comput. Math. 18 (2018), 703–730.  DOI: 10.1007/s10208-017-9351-2
• [64] E. Feireisl, M. Lukacova-Medvidova, S. Necasova, A. Novotny, B. She: Asymptotic preserving error estimates for numerical solutions of compressible Navier-Stokes equations in the low Mach number regime, IM-2016-49, SIAM Multiscale Model. Simul. 16 (2018), 150–183 DOI:10.1137/16M1094233
• [63] G. Bispen, M. Lukacova-Medvidova, L. Yelash: Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation, J. Comput. Phys. 335 (2017), 222-248. This manuscript version is made available under the CC-BY-NC-ND 4.0 license,  DOI: 10.1016/j.jcp.2017.01.020
• [62] M. Lukáčová-Medvid’ová, J. Rosemeier, P. Spichtinger, B. Wiebe: IMEX finite volume methods for cloud simulation, In: Cancès C., Omnes P. (eds) Finite Volumes for Complex Applications VIII – Hyperbolic, Elliptic and Parabolic Problems, Springer Proceedings in Mathematics  and Statistics,  Springer Proc. Math. Stat., 200, (2017) 179–187
• [61] M. Lukacova-Medvidova, H. Mizerova, S. Necasova, M. Renardy: Global existence result for the generalized Peterlin viscoelastic model, SIAM J. Math. Anal. 49 (2017), 2950–2964 DOI: 10.1137/16M1068505
• [60] M. Lukacova-Medvidova, H. Mizerova, H. Notsu, M. Tabata:  Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part I: A nonlinear scheme, ESAIM Math. Model. Numer. Anal. 51 (2017), 1637–1661. The original publication is available at www.esaim-m2an.org
• [59] M. Lukacova-Medvidova, H. Mizerova, H. Notsu, M. Tabata:  Numerical analysis of the Oseen-type Peterlin viscoelastic model by the stabilized Lagrange-Galerkin method, Part II: A linear scheme,  arXiv,  ESAIM Math. Model. Numer. Anal. 51 (2017), 1663–1689.  The original publication is available at www.esaim-m2an.org
• [58] N. Sfakianakis, N. Kolbe, N. Hellmann, M. Lukacova-Medvidova: A multiscale approach to the migration of cancer stem cells: mathematical modelling and simulations, B. Math. Biol. 79,(1), (2017), 209–235  DOI: 10.1007/s11538-016-0233-6
• [57] N. Kolbe, M. Lukacova-Medvidova, N. Sfakianakis, B. Wiebe: Numerical simulation of a contractivity based multiscale cancer invasion model, accepted to Multiscale Models in Mechano and Tumor Biology: Modeling, Homogenization and Applications, A. Gerisch et al. (Eds), Lecture Notes in Comp. Science Eng., Springer (2016)
• [56] M. Lukacova-Medvidova, H. Notsu, B. She: Energy dissipative characteristic schemes for the diffusive Oldroyd-B viscoelastic fluid,  Internat. J. Num. Methods Fluids 81(9) (2016), 523-557. DOI:10.1002/fld.4195
• [55] R.S. Lehmann, M. Lukacova-Medvidova, B.J.P. Kaus, A.A. Popov: Comparison of continuous and discontinuous Galerkin approaches for variable-viscosity Stokes flow, ZAMM, J. Appl. Math. Mech. 96(6) (2016), 733-746. DOI: 10.1002/zamm.201400274
• [54] N. Kolbe, J. Katuchova, N. Sfakianakis, N. Hellmann, M. Lukacova-Medvidova: A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: the urokinase model,  Appl. Math. and Comput. 273 (2016), 353-376, This manuscript version is made available under the CC-BY-NC-ND 4.0 license,  DOI: 10.1016/j.amc.2015.08.023
• [53] M. Lukacova-Medvidova, H. Mizerova, S. Necasova: Global existence and uniqueness result for the diffusive Peterlin viscoelastic model, Nonlinear Analysis: Theory, Methods and Appl. 120,  (2015), 154-170, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.na.2015.03.001
• [52] M. Lukacova-Medvidova, H. Mizerova, B. She, J. Stebel:  Error analysis of finite element and finite volume methods for some viscoelastic fluids, J. Numer. Math. 24(2) (2016), 105-123, DOI: 10.1515/jnma-2014-0057
• [51] A. Hundertmark-Zauskova, M. Lukacova-Medvidova, S. Necasova: On the weak solution of the fluid-structure interaction problem for shear-dependent fluids, Recent Developments of Mathematical Fluid Mechanics, H. Amann, Y. Giga, H. Kozono, H. Okamoto and M. Yamazaki (eds.), Series of Advanced in Mathematical Fluid Mechanics, Birkhauser Verlag (2014); DOI:10.1007/978-3-0348-0939-9_16
• [50] S. Noelle, G. Bispen, K. R. Arun, M. Lukacova-Medvidova, C.-D. Munz: A weakly asymptotic preserving low Mach number scheme for the Euler equations of gas dynamics, SIAM J. Sci. Comp. 36(6), (2014), 989-1024. DOI:10.1137/120895627
• [49] A. Hundertmark-Zauskova, M. Lukacova-Medvidova, S. Necasova: On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid, Journal of the Mathematical Society of Japan 68(1) (2016), 193-243. DOI: 10.2969/jmsj/06810193
• [48] M. Lukacova-Medvidova, N. Sfakianakis: Entropy dissipation of moving mesh adaptation, J. Hyper. Diff. Eqs. 11(3), (2014), 633-653, DOI:10.1142/S0219891614500192
• [47] L. Yelash, A. Mueller, M. Lukacova-Medvidova, F.X. Giraldo, V. Wirth: Adaptive discontinuous evolution Galerkin method for dry atmospheric flow, J. Comp. Phys. 268(1), (2014), 106-133, This manuscript version is made available under the CC-BY-NC-ND 4.0 license,  DOI: 10.1016/j.jcp.2014.02.034
• [46] G. Bispen, K.R. Arun, M. Lukacova-Medvidova, S. Noelle: IMEX large time step finite volume methods for low Froude number shallow water flows, CiCP 16, (2014), 307-347. DOI:10.4208/cicp.040413.160114a
• [45] C. Grandmont, M. Lukacova-Medvidova, S. Necasova: Mathematical and numerical analysis of some FSI problems, Book Chapter: „Fluid-structure interaction with multiple structural layers: theory and numerics,“ Invited Contribution to Book Series: „Advances in Mathematical Fluid Mechanics“ Eds. T. Bodnar, G.P Galdi, S. Necasova. Springer/Birkhauser (2014), 1-77.
• [44] A. Kurganov, M. Lukacova-Medvidova: Numerical study of two-species chemotaxis models, Discr. Cont. Systems, Series B, 19, no. 1, 131-152 (2014). DOI:10.3934/dcdsb.2014.19.131
• [43] M. Lukacova-Medvidova, G. Rusnakova, A. Hundertmark-Zauskova: Kinematic splitting algorithm for fluid-structure interaction in hemodynamics, Comput. Methods Appl. Mech. Engrg. 265,  (2013), 83-106, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.cma.2013.05.025
• [42] M. Dudzinski, M. Lukacova-Medvidova: Well-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts, J. Comput. Phys. 235 (2013), 82-113, This manuscript version is made available under the CC-BY-NC-ND 4.0 license,DOI: 10.1016/j.jcp.2012.10.037.
• [41]  K.R. Arun, M. Lukacova-Medvidova, Phoolan Prasad and S.V. Raghurama Rao: A second order accurate kinetic relaxation scheme for inviscid compressible flows, Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 2013, Volume 120/2013, 1-24. DOI:10.1007/978-3-642-33221-0_1
• [40] A. Corli, I. Gasser, M. Lukacova-Medvidova, A. Roggensack, U. Teschke: A multiscale approach to liquid flows in pipes I: The single pipe, Applied Mathematics and Computations 219(3), (2012), 856-874, This manuscript version is made available under the CC-BY-NC-ND 4.0 license,  DOI:10.1016/j.amc.2012.06.054
• [39] K. R. Arun, Maria Lukacova-Medvidova: A Characteristics based genuinely multidimensional discrete kinetic scheme for the Euler equations, J. Sci. Comp. 55(1), 2013, 40-64. DOI:10.1007/s10915-012-9623-6
• [38] M.D. Scharpenberg, M. Lukacova-Medvidova: Adaptive Gaussian particle method for the solution of the Fokker-Planck equation, ZAMM-Journal of Applied Mathematics and Mechanics 92(10), 770-781, 2012. DOI:10.1002/zamm.201100088
• [37] B.J. Block, M. Lukacova-Medvidova, P. Virnau, L. Yelash: Accelerated GPU simulation of compressible flow by the discontinuous evolution Galerkin method,  European Physical Journal Special Topics 210, 119-132, 2012
• [36] A. Hundertmark-Zauskova, M. Lukacova-Medvidova, G. Rusnakova: Fluid-structure interaction for shear-dependent non-Newtonian fluids, Topics in mathematical modeling and analysis, Necas Center for Mathematical Modeling,  Lecture notes, Volume 7, (2012),  109-158.
• [35] A. Hundertmark-Zauskova, M.Lukacova-Medvidova, F. Prill: Large time step finite volume evolution Galerkin methods,  J. Sci. Comp., 48, (2011), 227–240. DOI:10.1007/s10915-010-9443-5
• [34] M. Dudzinski, M.Lukacova-Medvidova: Well-balanced path-consistent finite volume EG schemes for the two-layer shallow water equations, Notes on Numerical Fluid Mechanics and Interdisciplinary Design, Springer, 2010. DOI:10.1007/978-3-642-17770-5_10
• [33] A. Bollermann, S.Noelle, M.Lukacova-Medvidova: Finite Volume Evolution Galerkin Methods for Shallow Water Equations with Dry Beds,  Comm. Comput. Physics 10(2), 371–404, 2011. DOI:10.4208/cicp.220210.020710a
• [32] K.R. Arun, M. Lukacova-Medvidova, and P. Prasad: Numerical: Front Propagation Using Kinematical Conservation Laws, book chapter in Finite Volumes for Complex Applications VI Problems & Perspectives (eds. J. Fort et al.), 49-57, 2011. DOI:10.1007/978-3-642-20671-9_6
• [31] K.R. Arun, M.Lukacova-Medvidova, S.V.Raghurama, Phoolan Prasad: An Application of 3D Kinematical Conservation Laws: Propagation of a Three Dimensional Wavefront , SIAM J.App.Math. 70(7), 2604-2626, 2010. DOI:10.1137/080732742
• [30] A.Hundertmark-Zauskova, M.Lukacova-Medvidova: Numerical Study of Shear-Dependent Non-Newtonian Fluids in Compliant Vessels , Computers and Mathematics with Applications 60, 572-590, 2010, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.camwa.2010.05.004
• [29] M.Lukacova-Medvidova, K.W. Morton: Finite Volume Evolution Galerkin Methods: A Survey, Indian J. Pure & Appl. Math. 41(2), 329-361, 2010. DOI:10.1007/s13226-010-0021-1
• [28] F. Prill, M.Lukacova-Medvidova, R. Hartmann: Smoothed Aggregation Multigrid for the Discontinuous Galerkin Method , SIAM J.Sci.Comp. 31(5), 3503-3528, 2009. DOI:10.1137/080728457
• [27] R. Hartmann, M.Lukacova-Medvidova, F. Prill: Efficient Preconditioning for Discontinuous Galerkin Finite Element Method by Low-Order Elements, Appl. Num. Math. 59(8), 1737-1753 , 2009, This manuscript version is made available under the CC-BY-NC-ND 4.0 license,   DOI: 10.1016/j.apnum.2009.01.002
• [26] K.R. Arun, M. Kraft, M.Lukacova-Medvidova, Phoolan Prasad: Finite Volume Evolution Galerkin Method for Hyperbolic Conservation Laws with Spatially Varying Flux Functions , J. Comp. Phys.,228(2), 565-590, 2009,This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.jcp.2008.10.004
• [25] M. Lukacova-Medvidova, A. Zauskova: Numerical Modelling of Shear-Thinning Non-Newtonian Fluids in Compliant Vessels, J. Num.Meth. Fluids 56(8), 2008, 1409-1415. DOI:10.1002/fld.1676
• [24] M. Lukacova-Medvidova, S. Noelle, M. Kraft: Well-balanced Finite Volume Evolution Galerkin Methods for the Shallow Water Equations, J. Comp. Phys. 221, 2007, 122-147, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI:10.1016/j.jcp.2006.06.015
• [23] M. Lukacova-Medvidova, G. Warnecke, Y. Zahaykah: Finite Volume Evolution Galerkin (FVEG) Methods for Three-Dimensional Wave Equation System, Appl. Num. Math.57(9), 2007, 1050-1064, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.apnum.2006.09.011
• [22] M. Lukacova-Medvidova, U. Teschke: Comparison Study of Some Finite Volume and Finite Element Methods for the Shallow Water Equations with Bottom Topography and Friction Terms, J.Appl. Mech. Math. (ZAMM) 86(11), 2006, 874-891. DOI:10.1002/zamm.200510280
• [21] M. Lukacova-Medvidova, G. Warnecke, Y.Zahaykah: On the Stability of the Evolution Galerkin Schemes Applied to a Two-dimensional Wave Equation System, SIAM J. Num. Anal.44(4), 2006, 1556-1583, DOI:10.1137/040615882
• [20] M. Lukacova-Medvidova, J. Saibertova-Zatocilova: Finite Volume Schemes for Multi-Dimensional Hyperbolic Systems Based on the Use of Bicharacteristics, Appl. Math.51(3), 2006, 205-228. DOI:10.1007/s10492-006-0012-z
• [19] T. Kröger, M. Lukacova-Medvidova: An Evolution Galerkin Scheme for the Shallow Water Magnetohydrodynamic (SMHD) Equations in Two Space Dimensions, J. Comp. Phys. 206, 2005, 122-149, This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI: 10.1016/j.jcp.2004.11.031
• [18] M.Lukacova-Medvidova, Z. Vlk: Well-balanced Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Source Terms, Int. J. Num. Fluids 47(10-11), 2005, 1165-1171. DOI:10.1002/fld.855
• [17] M.Lukacova-Medvidova, K.W. Morton G.Warnecke: Finite Volume Evolution Galerkin (FVEG) Methods for Hyperbolic Systems, SIAM J. Sci. Comp. 26(1), 2004, 1-30. DOI:10.1137/S1064827502419439
• [16] M.Lukacova-Medvidova, G.Warnecke, Y.Zahaykah: On the Boundary Conditions for EG-methods Applied to the Two-Dimensional Wave Equation Systems, ZAMM 84(4), 2004, 237-251. DOI:10.1002/zamm.200310103
• [15] M. Lukacova-Medvidova, J. Saibertova, G. Warnecke, Y. Zahaykah: On evolution Galerkin Methods for the Maxwell and the Linearized Euler Equations, Appl. Math. 49(5), 2004, 415-439, DOI: 10.1023/B:APOM.0000048121.68355.2a
• [14] M. Lukacova-Medvidova, G. Warnecke, Y. Zahaykah: Third Order Finite Volume Evolution Galerkin (FVEG) Methods for Two-Dimensional Wave Equation System, J. Numer. Math 11(3), 2003, 235-251. DOI:10.1163/156939503322553108
• [13] J. Li, M. Lukacova-Medvidova, G. Warnecke: Evolution Galerkin Schemes for the Two-dimensional Riemman Problems, Discrete and Continuous Dynamical Systems (Series A) 9(3), 2003, 559-576, Doi: 10.3934/dcds.2003.9.559
• [12] M. Lukacova-Medvidova, J. Saibertova, G. Warnecke: Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems, J. Comp. Phys. 183, 2002, 533-562,  This manuscript version is made available under the CC-BY-NC-ND 4.0 license, DOI:10.1006/jcph.2002.7207
• [11] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Finite Volume Evolution Galerkin Methods for Euler Equations of Gas Dynamics, Int. J. Numer. Meth. Fluids 40(3-4), John Wiley & Sons, 2002, 425-434.
• [10] M. Lukacova-Medvidova, G. Warnecke: Lax-Wendroff Type Second Order Evolution Galerkin Methods for Multidimesnional Hyperbolic Systems, Journal of Num. Mathematics 8(2), 2000, 127-152.
• [9] S. Matusu-Necasova, M. Lukacova-Medvidova: On Stability of Bipolar Barotropic Non-Newtonian Compressible Fluids, Mathematical Modelling and Numerical Analysis 34(5), 2000, 923-934, DOI: 10.1051/m2an:2000109,  The original publication is available at www.esaim-m2an.org
• [8] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Evolution Galerkin Methods for Hyperbolic Systems in Two Space Dimensions, MathCom. 69(232), 2000, 1355-1384. DOI:10.1090/S0025-5718-00-01228-X 
• [7] M. Feistauer, J. Felcman, M. Lukacova-Medvidova, G. Warnecke: Error Estimates of a Combined Finite Volume-Finite Element Method for Nonlinear Convection-Diffusion Problems, SIAM J. Numer. Anal. 36 (5), 1999, 1528-1548, DOI: 10.1137/S0036142997314695
• [6] S. Matusu-Necasova, M. Lukacova-Medvidova: Bipolar Isothermal Non-Newtonian Compressible Fluids, J. Math. Anal. Appl., 225, 1998, 168-192,This manuscript version is made available under the CC-BY-NC-ND 4.0 license,  DOI: 10.1006/jmaa.1998.6014
• [5] M. Lukacova-Medvid’ova: Combine Finite Element – Finite Volume Method (Convergence Analysis), Comment. Math. Univ. Carolinae 38(4), 1997, 717-741.
• [4] S. Matusu-Necasova, M. Lukacova-Medvidova: Some Models of Non-Newtonian Fluids and their Properties, ZAMM 77, S1, 1997, 205-206.
• [3] M. Feistauer, J. Felcman, M. Lukacova-Medvidova: On the Convergence of a Combined Finite Volume-Finite Element Method for Nonlinear Convection-Diffusion Problems, Numer. Methods for Partial Differ. Equations 13, 1997, 163-190. DOI:10.1002/(SICI)1098-2426(199703)13:2<163::AID-NUM3>3.0.CO;2-N
• [2] M. Feistauer, J. Felcman, M. Lukacova-Medvidova: Combined Finite Element-Finite Volume Solution of Compressible Flow, Journal of Comput. and Appl.Math. 63, 1995, 179-199,   DOI: 10.1016/0377-0427(95)00051-8
• [1] S. Matusu-Necasova, M. Medvidova: Bipolar Barotropic Nonnewtonian Fluid, Comment. Math. Univ. Carolina 35 (3), 1994, 467-483.

Conference proceedings

• [31] M. Lukacova-Medvidova: K-convergence of finite volume solutions of the Euler equations, In: Finite Volumes for Complex Applications IX, Springer Proceedings in Mathematics & Statistics (Ed. Klöfkorn et al.), 2020, 25-37.
• [30] N. Emamy, M. Lukacova-Medvidova, S. Stalter, P. Virnau, L. Yelash: Reduced-order hybrid multiscale method combining the Molecular Dynamics and the Discontinuous-Galerkin method, VII ECCOMAS Conference, Coupled Problems, Papadrakakis et al. (eds), (2017), 1-15.
• [29] G.Bispen, M. Lukacova-Medvidova, L.Yelash: IMEX finite volume evolution Galerkin method for three-dimensional weakly compressible fluids, Proceedings of the Algoritmy,eds. Handlovicova et al., 2016, 62-73, ISBN 978-80-227-4544-4.
• [28] F.Prill, M. Lukacova-Medvidova, R. Hartmann: A Multilevel Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations , Proceedings of the Algoritmy,eds. Handlovicova et al., 2009, 91-101, ISBN 978-80-227-3032-7.
• [27] A. Bollermann, M. Lukacova-Medvidova, S. Noelle: Well-Balanced Finite Volume Evolution Galerkin Methods for 2D Shallow Water Equations on Adaptive Grids, Proceedings of the Algoritmy,eds. Handlovicova et al., 2009, 81-91, ISBN 978-80-227-3032-7.
• [26] M. Lukacova-Medvidova, E. Tadmor: On the Entropy Stability of the Roe-type Finite Volume Methods , Proceedings of Symposia in Applied Mathematics 67, Part 2, 765-774, 2009. DOI:10.1090/psapm/067.2/2605272
• [25] M. Scharpenberg, M. Lukacova-Medvidova: Stochastic Considerations for Dynamic Systems, 12th AIAA Multidisciplinary Analysis and Optimization Conference, 2008.
• [24] M. Kraft, M. Lukacova-Medvidova: Numerical Aspects of Parabolic Regularization for Resonant Balance Laws, Proceedings of HYP 2006 Hyperbolic Problems: Theory, Numerics, Applications Springer Verlag, (eds. S. Benzoni-Gavage, D. Serre), 2008, 695-702. DOI:10.1007/978-3-540-75712-2_70
• [23] A. Zauskova, M. Lukacova-Medvidova: Numerical Modelling of Shear-Thinning Non-Newtonian Flows in Compliant Vessels, Proceedings of ICIAM 2007, Zürich 2007.
• [22] M. Lukacova-Medvidova, A. Zauskova: Mathematical Modelling and Numerical Simulation of Blood Flow in Compliant Vesselsof Blood Flow in Compliant Vessels, Proceedings of ECCOMAS 2008, Venice 2008.
• [21] K.R.Arun, S.V. Ragurama Rao, M. Lukacova-Medvidova, Ph. Prasad: A Genuinely Multi-dimensional Relaxatioan Scheme for Hyperbolic Conservation Laws Proceedings of the 7th Asian Computational Fluid Dynamics Conference, Bangalore 2007.
• [20] M. Lukacova-Medvidova, A. Zauskova: Numerical Modelling of Complex Flow in Compliant VesselsVessels, 6 pages, Proceedings of the ICFD Conference Reading, 2007.
• [19] M. Scharpenberg, M. Lukacova-Medvidova: Use of Automatic Differentiation for Sensitivity Analysis of Flight Loads, , Proceedings of Workshop on Aicraft Systems and Technologies, Hamburg, (ed. O. von Estorff),2007, 407-414, ISBN 978-3-8322-6046-0.
• [18] K. Baumbach, M. Lukacova-Medvidova: On the Comparison of Evolution Galerkin and Discontinuous Galerkin Schemes, 2006, 16 pages, Proceedings of International Workshop on Computational Science and its Education, Beijing 2005. DOI:10.1142/9789812792389_0005
• [17] M. Lukacova-Medvidova: Numerical Modeling of Shallow Flows Including Bottom Topography and Friction Effects , Proceedings of Algoritmy 2005, Slovakia, (eds. Handlovicova et al.), 2005, 73-82, ISBN 80-227-2192-1.
• [16] M. Lukacova-Medvidova, Z.Vlk: Well-balanced Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Source Terms, Proceedings ICFD Conference, Oxford University Computing Laboratory, 2004, 6 pages
• [15] M. Lukacova-Medvidova, J. Saibertova: Genuinely Multidimensional Evolution Galerkin Schemes for the Shallow Water Equations, Numerical Mathematics and Advanced Applications, ENUMATH, 2002, 105-114. DOI:10.1007/978-88-470-2089-4_13
• [14] M. Lukacova-Medvidova: Multidimensional Bicharacteristics Finite Volume Methods for the Shallow Water Equations, Finite Volumes for Complex Applications, Hermes, 2002, 389-397
• [13] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Finite Volume Evolution Galerkin Methods for Euler Equations of Gas Dynamics, Numerical Methods for Fluid Dynamics VII, ICFD, Oxford University Computing Laboratory (ed. M.J.Baines), Will Print Oxford, 2001, 413-421
• [12] M. Lukacova-Medvidova, L. Grigerek, S. Necasova: Numerical Solution of Bipolar Barotropic Non-Newtonian Fluids, Fourth Conference on Numerical Modelling in Continuum Mechanics (eds. M. Feistauer et al.), Matfyzpress Praha 2001, 135-143.
• [11] M. Lukacova-Medvidova, G. Warnecke, Y. Zahaykah: Numerical Schemes Based on Bicharacteristics for Hyperbolic Systems, International Conference CIMASI’2000, Casablanca, Marocco.
• [10] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Evolution Galerkin Methods for Multidimensional Hyperbolic Systems, European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000 (eds. Onate et al.), CIMNE 2000, 1-14
• [9] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Finite Volume Evolution Galerkin Schemes for Multidimensional Hyperbolic Systems, Proceedings of the Godunov Conference (ed. E.F. Toro), Oxford 1999, Kluwer, 2000. DOI:10.1007/978-1-4615-0663-8_56
• [8] .M. Lukacova-Medvidova, G. Warnecke, Y. Zahaykah: Evolution Galerkin Methods for the Multi-dimensional Wave Equation System, Proceedings of the International Symposium on Electromagnetic Compatibility (eds. J. Nitsch et al.), Magdeburg, 67-72.
• [7] M. Lukacova-Medvidova, K. W. Morton, G. Warnecke: High-Resolution Finite Volume Evolution Galerkin Schemes for Multidimensional Hyperbolic Conservation Laws, 3.rd European Conference on Numerical Mathematics and Advanced Applications, Jyväskylä, Finland, 633-640.
• [6] M. Lukacova-Medvidova, K. W. Morton, G. Warnecke: Finite Volume Evolution Galerkin Methods for Multidimensional Hyperbolic Problems, Finite Volumes for Complex Applications (ed. R. Vilsmeier et al.), Hermes, 1999, 289-296.
• [5] M. Lukacova-Medvidova, K.W. Morton, G. Warnecke: Evolution Galerkin Methods Multidimensional Hyperbolic Systems, 2.nd European Conference on Numerical Mathematics and Advanced Applications (eds. H.G. Bock et al.) World Scientific Publishing Company, Singapore, 1998, 445-452.
• [4] M. Lukacova-Medvidova: Numerical Solution of Compressible Flow, Conference on Differential Equations and their Applications (CDROM), EQUADIFF 9, (eds. Z. Dosla et al.), Masaryk University Brno, 1997, 201-210.
• [3] M. Lukacova-Medvidova: Numerical Solution of Compressible Flow, Proceedings of the Conference on Analysis, Numerics and Applications of Differential and Integral Equations, Stuttgart, 1996.
• [2] M. Lukacova-Medvidova: Error Estimate for Combined Finite Element-Finite Volume Methode, 2.nd International seminar: Euler and Navier-Stokes Equations (eds. K. Kozel et al.), Institute of Thermodynamics, Czech Academy of Sciences, Praha, 1996, 51-52.
• [1] M. Lukacova : Kombiniertes Finite-Element-Finite-Volume-Verfahren zur Lösung der kompressiblen Navier-Stokes-Gleichungen, 7. STAB Workshop, DLR Göttingen, 1995.

Thesis

• [2] Mathematical modelling of compressible flow, Habilitation, 1998, Technical University Brno.
• [1] Numerical solution of compressible flow, Dissertation, 1994, Charles University Prague.

Preprints/submitted papers

• [2] M. Lukacova-Medvidova: On the error estimate of a combined finite element – finite volume method, Otto-von-Guericke-Uni Magdeburg, Preprint Nr.9, 1996, pp. 19.
• [1] J. Felcman, M. Lukacova, G. Warnecke, W.L. Wendland : Adaptive Mesh Refinement for Euler Equations, Bericht 95-15, research report Mathematisches Institut A, Universität Stuttgart, Germany, 1995, pp. 22.

Organisation of Workshops and Conferences

• CIRM Workshop: Mathematical Models for Mixtures, together with C. Cances, V.Erhlacher, P. Farrell, 2026
• BRIN Workshop: Structure-Preserving Numerical Methods for Nonlinear PDEs with Uncertainty, together with A. Chertock, A. Kurganov, 2026.
• Int. Conference Hyperbolic Problems: Theory, Numerics and Applications, Stuttgart, together with C. Rohde, 2026.
• Conference Numerical Methods for Hyperbolic Problems, Darmstadt, together with J. Giesselmann, 2025.
• Workshop Hyperbolic Balance Laws: Interplay between Scales and Randomness,Mathematical Research Institute Oberwolfach, together with R. Abgrall, M. Gravello, February 2024.
• Sino-German Workshop. Recent Advances in Hyperbolic Balance Laws, Capital Normal University, Beijing, together with B. She, G. Warnecke and S. Jiang, September 2023
• Workshop Hyperbolic Balance Laws and Beyond, 29.6.-1.7.2022, Magdeburg, together with C. Helzel, M. Hantke, F. Thein
• Minisymposium Recent Advances on Analysis and Numerics of Multidimensional Compressible Flows, SIAM conference on Partial Differential Equations, 14.3.-18.3. 2022, Berlin, together with E. Feireisl
• Workshop Inverse Problems and Beyond, 22.10.2021, Mainz, together with B. von Harrach
• Oberwolfach Small Collaborative Workshop on Advanced Numerical Methods for Nonlinear Hyperbolic Balance Laws and their Applications, 29.8.- 4.9. 2021, MFO Oberwolfach, together with S. Jiang, J. Li and G. Warnecke
• Oberwolfach Workshops on Hyperbolic Balance Laws: modelling, analysis, and numerics,  28.3.-6.3. 2021, MFO Oberwolfach,  together with R. Abgrall, M. K. Trivisa, M. Garavello
• Minisymposium Numerical Simulations of Fluid Flows, Algoritmy 10.-15.9. 2020, Vysoke Tatry, Podbanske, Slovakia, together with M. Feistauer
• Minisymposium Multiscale and stochastic numerical methods for hyperbolic conservation laws, together with A. Chertock and A. Kurganov, ICIAM, Valencia 2019
• Conference Selected topics in transport phenomena: deterministic and probabilistic aspects, together with A. Chertock and E. Tadmor, Center for Scientific Computation and Mathematical Modeling, University of Maryland, 18.-21.4.2017
• Conference on Recent Advances in Analysis and Numerics of Hyperbolic Conservation Laws, together with C. Helzel and M. Hantke, 8.-10.9. 2016, Magdeburg
•  Minisymposium Numerics for conservation laws and nonlinear convection-diffusion problems, together with M. Feistauer, Algoritmy 2016, 13.-18.3.2016
• Workshop Women in Applied Math & Soft Matter Physics, together with S. Jabbari and F. Schmid, 25.-18.10.2015, Schloss Waldthausen, Mainz
• Minisymposium „Recent Developments  in Modeling and Numerical Simulations of Geophysical Flows„, together with A. Chertock and A. Kurganov,  ICIAM 2015, 10.-14.8.2015, Beijing
• CECAM Workshop „Multiscale Simulation Methods for Soft Matter Systems„, together with F. Schmid, B. Dünweg, K. Kremer and F. Müller-Plathe, 6.-8.10.2014, Mainz
• Sino-German Symposium „Modern Numerical Methods for Compressible Fluid Flows and Related Problems“, together with Jiequan Li,  21.5.-27.5.2014, Beijing, China, supported by the Sino-German Center for Research Promotion
• Minisymposium „Analysis and Numerics of Fluid-Structure Interaction“, Equadiff 2013, 26.8.-30.8.2013 Prague
• Workshop „Modelling, Optimization and Simulation of Complex Fluid Flow“together with D. Bothe, S. Ulbrich and M. Schäfer, TU Darmstadt, 20.-22.6. 2012
• Minisymposium „Finite volume und finite element schemes for fluid-structure interaction“  together with M. Feistauer, ALGORITMY 2012, Podbanske, Slovakia, 9.-14.9.2012
• Workshop „Efficient mesh adaptation methods for evolution problems: theory and applications„  together with N. Sfakianakis, WPI, University of Vienna, 14-17.12. 2011
• Workshop „Modelling and Numerics of Conservation Laws“  University of Mainz, 16.2. 2011
• Minisymposium on “ Advances in Numerical Modelling of Advection and Convection Dominated Flows „ together with S.Karabasov (Cambridge University)
  9th World Congress on Computational Mechanics, Australia, 19. – 23.7. 2010
• Minisymposium on „Recent Advances in Numerics of Hyperbolic Conservation Laws and Related Problems“ ALGORITMY 2009, Podbanske Slovakia
• Second Annual Summer School „EU Doctoral School: Differential Equations in Science and Engineering „ together with I. Gasser (Uni-Hamburg), Hamburg 2008
• Minisymposium on „Recent Advances in Numerical Methods for Hyperbolic Problems“ together with S. Karabasov (Cambridge), IACM/ECCOMAS Congress,Venice 2008
• Minisymposium on „Navier Stokes Equations and Related Conservation Laws„together with M. Feistauer (Prag), Slovak-Austrian Mathematical Congress, 16.-21.09.2007, Podbanske, Slovakia
• Minisymposium on „Partial Differential Equations with Inherent Conditions“ together with R. Jeltsch (ETH Zürich) and J. Mac Hyman (Iowa State University), 2nd Joint Meeting of AMS, DMV, OMG, Mainz 2005
• Workshop on „Multi-Dimensional Wave Structures in Hyperbolic Systems„ together with S. Noelle (Aachen) and G. Warnecke (Magdeburg); TU Hamburg-Harburg, 2004

Themen für Masterarbeiten:

In meiner AG beschäftigen wir uns mit der Entwicklung von modernen, effizienten Verfahren für verschiedene Evolutionsgleichungen (d.h. zeitabhängige partielle Differentialgleichungen). Aktuelle Forschungsthemen widmen sich z.B. der Modellierung von Blutströmung, Fluid-Struktur-Wechselwirkung, langen-Zeitschrittverfahren für hyperbolische Erhaltungsgleichungen mit Anwendungen in der Meteorologie und Geophysik, Hybriden-Mehrskalenverfahren für Polymere.

Im Folgenden finden Sie einige Beispiele für mögliche Abschlussarbeiten. Auf Anfrage können weitere Themen zu den o.g. Forschungsschwerpunkten vergeben werden. Vorkenntnisse aus den Numerik-Vorlesungen werden erwartet.

• Hybride Mehrskalenverfahren
• Semi-implizite Verfahren für nichtlineare skalare hyperbolische Gleichungen
• Modellierung und Simulation von komplexen Fluiden
• Numerische Analyse von Euler und Navier-Stokes Gleichungen: relative Entropie, Masswertige Lösungen

Übersicht der Lehrveranstaltungen:

Sommersemester 2026

• Hauptseminar: Wave Motion
• Modelling Lab
• Nichtlineare Funktionalanalysis

Wintersemester 2025/26

• Functional Analysis in Action: Computational Fluid Dynamics
• Hauptseminar: Mathematische Modellierung
• Hauptseminar: Mathematics of Machine Learning

Sommersemester 2025

Forschungsfreisemester im Rahmen von Gutenberg Forschungskolleg

• Oberseminar Numerik

Wintersemester 2024/25

• Analysis and Numerics of Conservation Laws / Analysis und Numerik von Erhaltungsgleichungen
• Hauptseminar: Mathematische Modellierung
• Hauptseminar: Mathematics for Machine Learning

Sommersemester 2024

Forschungsfreisemester im Rahmen von Gutenberg Forschungskolleg

• Oberseminar Numerik

Wintersemester 2023/24

• Vorlesung: Numerik partieller Differentialgleichungen
• Vorlesung: Computational Fluid Dynamics
• Hauptseminar: Stochastische Techniken in mathematischer Modellierung
• Oberseminar Numerik

Sommersemester 2023

Forschungsfreisemester im Rahmen von Gutenberg Forschungskolleg

• Oberseminar Numerik

Wintersemester 2022/23

• Hauptseminar: Datenbasierte mathematische Modellierung
• Vorlesung: Numerik gewöhnlicher Differentialgleichungen
• Vorlesung: Mathematical Fluid Dynamics
• Oberseminar Numerik

Sommersemester 2022

• Mathematik für Naturwissenschaftler I
• Modellierungspraktikum
• Oberseminar Numerik

Wintersemester 2021/22

• Vorlesung: Numerik partieller Differentialgleichungen
• Vorlesung: Nichtlineare Funktionalanalysis
• Hauptseminar: Datenbasierte mathematische Modellierung
• Oberseminar Numerik

Sommersemester 2021

Forschungsfreisemester im Rahmen von Gutenberg Forschungskolleg

• Oberseminar Numerik

Wintersemester 2020/21

• Vorlesung: Numerik partieller Differentialgleichungen
• Hauptseminar: Mathematische Modellierung
• Vorlesung: Computational Fluid Dynamics
• Oberseminar Numerik

Wintersemester 2019/20 und Sommersemester 2020

Forschungsfreisemester
visiting Institute of Appl. Physics and Comput. Mathematics, Beijing &  University of Hong Kong,Hong Kong

• Oberseminar Numerik

Sommersemester 2019

• Hauptseminar: Mathematische Modellierung
• Vorlesung: Computational Fluid Dynamics
• Vorlesung: Mathematik für Naturwissenschaftler II

• Vorlesung des Gastdozenten Prof. RNDr. Eduard Feireisl, DrSc.: Oscillatory Solutions to Equations in Fluid Dynamics

Wintersemester 2018/19

• Vorlesung: Numerik gewöhnlicher Differentialgleichungen
• Hauptseminar: Mathematische Modellierung
• Hauptseminar: Stochastische Techniken in mathematischer Modellierung

Sommersemester 2018

• Vorlesung: Analysis und Numerik von Erhaltungsgleichungen
• Hauptseminar: Mathematische Modellierung komplexer Flüssigkeiten
• Modellierungspraktikum: Numerische Modellierung dynamischer Zufallsprozesse
• Oberseminar Numerik

Wintersemester 2017/18

• Vorlesung: Mathematical Fluid Dynamics
• Hauptseminar: Moderne Simulationsmethoden
• Vorlesung: Numerik partieller Differentialgleichungen
• Oberseminar Numerik

Sommersemester 2017

• Vorlesung: Mathematik für Naturwissenschaftler II
• Vorlesung: Computational Fluid Dynamics
• Hauptseminar: Eine Einladung in die Mathematik
• Oberseminar Numerik

Wintersemester 2016/17

• Vorlesung: Mathematik für Naturwissenschaftler I
• Vorlesung: Nichtlineare Funktionalanalysis
• Hauptseminar: Wellenphänomene
• Oberseminar Numerik

Sommersemester 2016

• Vorlesung: Grundlagen der Numerik
• Modellierungspraktikum: Mathematische Modellierung der Strukturbildung
• Hauptseminar: Stochastische Techniken in mathematischer Modellierung
• Oberseminar Numerik

Wintersemester 2015/16

• Vorlesung: Computational Fluid Dynamics
• Hauptseminar: Eine Einladung in die Mathematik
• Hauptseminar: Moderne Simulationsmethoden
• Oberseminar Numerik

Sommersemester 2015

Forschungsfreisemester

Oberseminar Numerik

Wintersemester 2014/15

• Vorlesung: Analysis und Numerik von Erhaltungsgleichungen II
• Vorlesung: Numerik partieller Differentialgleichungen
• Oberseminar Numerik

Sommersemester 2014

• Vorlesung: Analysis und Numerik von Erhaltungsgleichungen
• Vorlesung: Nichtlineare Funktionalanalysis
• Hauptseminar: Komplexe Flüssigkeiten
• Lecture: Particle Methods for Nonlinear Partial Differential Equations (visiting Prof. Chertock)
• Oberseminar Numerik

Wintersemester 2013 /14

• Vorlesung: Numerik gewöhnlicher Differentialgleichungen
• Vorlesung: Computational Fluid Dynamics
• (Pro-)Seminar: Eine Einladung in die Mathematik
• Oberseminar Numerik

Sommersemester 2013

• Vorlesung: Grundlagen der Numerik
• Vorlesung: Mathematik für Naturwissenschaftler II
• Oberseminar Numerik

Wintersemester  2012/13

• Vorlesung: Mathematical Fluid Dynamics
• Vorlesung: Mathematik für Naturwissenschaftler I
• Hauptseminar: Lineare und Nichtlineare Wellenphänomene
• Oberseminar Numerik

Sommersemester 2012

• Vorlesung: Numerik und Analysis von Erhaltungsgleichungen
• Hauptseminar: Finite-Volumen-Methode
• Modellierungspraktikum: Mathematische Biologie
• Oberseminar Numerik

Wintersemester 2011/12

• Vorlesung: Numerik Partieller Differentialgleichungen
• Hauptseminar: Mathematische Biologie
• Vorlesung: Mathematical Fluid Dynamics
• Oberseminar Numerik

Sommersemester 2011

• Hauptseminar: Fluid-Struktur-Wechselwirkung
• Modellierungspraktikum: Hämodynamik
• Vorlesung: Numerics of nonlinear partial differential equations

Wintersemester 2010/11

sabbatical semester

Sommersemester 2010

• Hauptseminar: Wellenphänomene, Universität Mainz
• Vorlesung: Computational Fluid Dynamics, Universität Mainz
• Vorlesung:  Grundlagen der Numerik, Universität Mainz

Lecture Notes on Computational Methods in Fluid Dynamics
Gallery of Fluid Flow Images
The Virtual Album of Fluid Motion

Sommersemester 2006

sabbatical semester
visiting Center for Scientific Computation and Mathematical Modeling, University of Maryland

Sommersemester 2003-2005, 2007-2009

Mathematics II (General Engineering Science), TU Hamburg-Harburg
Numerical Modelling in Fluid Dynamics I (Finite Volume Methods / inviscid flows), TU Hamburg-Harburg

Wintersemester 2002/03-2009/10

Mathematics I (General Engineering Science), TU Hamburg-Harburg
Numerical Modelling in Fluid Dynamics II (Finite Element Methods / viscous flows), TU Hamburg-Harburg

• Seminar for Mathematics: Wave Motion (WS 2004/05) , TUHH
• Seminar for Mathematics: Multiscale Methods (WS 2005/06) , TUHH
• Seminar for Mathematics: Stochastic Tools in Mathematics and Science (WS 2006/07, WS 2007/08) , TUHH

Sommersemester 2002

Sophia Kovalevskaja Gastprofessorin, Universität Kaiserslautern

1996 – 2001

Numerics I, Mathematics III (ODE, PDE), Computational Fluid Dynamics, Technical University Brno, Czech Republic