Recent Publications | Numerical Mathematics

Book

E. Feireisl, M. Lukacova-Medvidova, H. Mizerova, B. She: Numerical Analysis of Compressible Fluid Flows, Modelling, Simulation and Application, Springer, 2021.

Journals

[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] Feireisl, E., Lukáčová-Medvid’ová, M., 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, 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, 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 13,
2806 (2021).
[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 10.1093/imanum/drz045
[78] E. 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(3) (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, 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 (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.
[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, 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.