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[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 Vessels Vessels, 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.
Prof. Dr. Mária Lukácová
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