Václav Kučera
Charles University
Prague, Czech Republic


doc. RNDr. Václav Kučera, Ph.D.
Sokolovská 83
186 75 Praha 8 - Karlín
Czech Republic

Tel. :   [+420] 9 5155 3362
e-mail: kucera@karlin.mff.cuni.cz


List of publications



ResearcherID profile:  D-3469-2012

Publications in journals

  1. L. Vacek, C.-W. Shu, V. Kučera: Discontinuous Galerkin method with Godunov--like numerical fluxes for traffic flows on networks Part I: L2 stability, Appl. Math. (to appear).
  2. L. Vacek, C.-W. Shu, V. Kučera: Discontinuous Galerkin method with Godunov--like numerical fluxes for traffic flows on networks Part II: Maximum principle, Appl. Math. (to appear).
  3. L. Vacek, V. Kučera: Godunov-like numerical fluxes for conservation laws on networks, J. Sci. Comput. 97 (70), 2023.
  4. S. Korotov, M. Křížek, V. Kučera: On degenerating finite element tetrahedral partitions, Numer. Math. 152(2), 307–329, 2022
  5. V. Kučera, M. Lukáčová-Medviďová, S. Noelle, J. Schütz: Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations, Numer. Math. 150(1), 79-103, 2022, arXiv:2011.13753.
  6. L. Vacek, V. Kučera: Discontinuous Galerkin method for macroscopic traffic flow models on networks, Comm. Appl. Math. Comput. 4(3), 986-1010, 2022, arXiv:2011.10862.
  7. V. Kučera, C.-W. Shu: On the time growth of the error of the DG method for advective problems, IMA J. Numer. Anal. 39 (2), 687-712, 2019, arXiv:1711.09417.
  8. A. Živčáková, V. Kučera: Discontinuous Galerkin method for a nonlocal hydrodynamic model of flocking dynamics, J. Comp. Phys. 372: 500-523, 2018.
  9. V. Kučera, M. Vlasák: A priori diffusion-uniform error estimates for nonlinear singularly perturbed problems: BDF2, midpoint and time DG, ESAIM: M2AN 51 (2), 537-563, 2017.
  10. V. Kučera: Finite element error estimates for nonlinear convective problems, J. Numer. Math. 24(3), 143-165, 2016.
  11. V. Kučera: Several notes on the circumradius condition, Appl. Math. 61(3), 287-298, 2016.
  12. V. Kučera: On diffusion-uniform error estimates for the DG method applied to singularly perturbed problems, IMA J. Numer. Anal. 34(2), 820-861, 2014.
  13. M. Feistauer, J. Hasnedlová, J. Horáček, A. Kosík, V. Kučera: Numerical simulation of fluid–structure interaction of compressible flow and elastic structure, Computing 95(1), 343-361, 2013. 
  14. M. Feistauer, J. Hasnedlová-Prokopová, J. Horáček, A. Kosík, V. Kučera: DGFEM for Dynamical Systems Describing Interaction of Compressible Fluid and Structures, J. Comput. Appl. Math. 254,  17-30, 2013. 
  15. J. Česenek, M. Feistauer, J. Horáček, V. Kučera, J. Prokopová: Simulation of compressible viscous flow in time-dependent domains, Appl. Math. Comput. 219(13),  7139-7150, 2013.
  16. M. Feistauer, J. Horáček, V. Kučera, J. Prokopová: On numerical solution of compressible flow in time-dependent domains, Mathematica Bohemica, vol. 137(1), 1-16, 2012.
  17. M. Feistauer, V. Kučera, K. Najzar and J. Prokopová: Analysis of Space-Time Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems, Numer. Math. 117:251–288, 2011. 
  18. V. Kučera, M. Feistauer, J. Prokopová: Discontinuous Galerkin Solution of Compressible Flow in Time Dependent Domains, Math. Comput. Simulat. 80:1612-1623, 2010.
  19. J. Prokopová, M. Feistauer, J. Horáček, V. Kučera: Numerical simulation of airflow through the model of oscillating vocal folds. Applied and Computational Mechanics 4: 215-224, 2010.
  20. V. Kučera: Optimal $L^\infty(L^2)$-error Estimates for the DG Method Applied to Nonlinear Convection-Diffusion Problems with Nonlinear Diffusion. Numer. Func. Anal. Opt. 31(3): 285 – 312, 2010.
  21. M. Feistauer, V. Dolejší, V. Kučera, V. Sobotíková: L-infinity(L-2)-error estimates for the DGFEM applied to convection-diffusion problems on nonconforming meshes, J. Numer. Math. 17(1): 45-65, 2009.
  22. V. Dolejší, M. Feistauer, V. Kučera, V. Sobotíková: An optimal $L^\infty(L^2)$-error estimate for the discontinuous Galerkin approximation of a nonlinear non-stationary convection–diffusion problem, IMA J. Numer. Anal. 29(3): 496-521, 2008.
  23. M. Feistauer, V. Kučera: Analysis of the DGFEM for nonlinear convection-diffusion problems, Electron. T. Numer. Ana. 32 (1): 33-48, 2008.
  24. M. Feistauer, V. Kučera: On a robust discontinuous Galerkin technique for the solution of compressible flow, J. Comput. Phys. 224: 208-221, 2007.
  25. M. Feistauer, V. Dolejší, V. Kučera: On the Discontinuous Galerkin Method for the Simulation of Compressible Flow with Wide Range of Mach Numbers, Computing and Visualization in Science 10: 17-27, 2007.

Preprints and submitted papers

  1. A. Quiriny, V. Kučera, J. Lambrechts, N. Moës, J.-F. Remacle: The Tempered Finite Element Method, J. Comput. Phys. (submitted), arXiv:2411.17564
  2. V. Kučera: On necessary and sufficient conditions for finite element convergence, Numer. Math. (submitted), arXiv:1601.02942

Selected conference proceedings

  1. L. Vacek, V. Kučera: Numerical solution of traffic flow models, Proc. of Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021, 1069-1078.
  2. V. Kučera, C.-W.Shu: Exponential Scaling and the Time Growth of the Error of DG for Advection-Reaction Problems, Proc. of ENUMATH 2017, 963-971, 2019.
  3. Z. Bílková, J. Soukup, V. Kučera: Cell Segmentation Using Level Set Methods with a New Variance Term, 13th International Conference, ICIAR 2016, A. Campilho et al. (eds.), Springer International (2016): 183-190.
  4. V. Kučera, A. Živčáková: Semi-implicit DGM applied to a model of flocking, Lecture Notes in Computational Science and Engineering 112, Proc. of ENUMATH 2015, 185-193, 2016.
  5. V. Kučera: A note on necessary and sufficient conditions for convergence of the finite element method, Proc. of Applications of Mathematics 2015, CAS, Prague, pp. 132-139, 2015.
  6. V. Kučera, A. Živčáková: Numerical Solution of a New Hydrodynamic Model of Flocking Dynamics, Programs and Algorithms of Numerical Matematics 17, pp. 124-129, 2015.
  7. V. Kučera: Error Estimates for Nonlinear Convective Problems in the Finite Element Method, Proc. of  Programs and Algorithms of Numerical Mathematics 16, pp. 236-141, 2013.
  8. V. Kučera, M. Vlasák: A Prioiri Diffusion-uniform Error Estimates for Singularly Perturbed Problems: Midpoint DG Discretization, Proc. of  Programs and Algorithms of Numerical Mathematics 16 Pages: 202-208, 2013.
  9. V. Kučera: Higher-Order Reconstruction: From Finite Volumes to Discontinuous Galerkin. Proc. of FVCA 6, Finite Volumes for Complex Applications VI Problems and Perspectives, Springer Berlin Heidelberg, 613-621, 2011.
  10. V. Kučera: On the Use of Reconstruction in Higher Order DG Schemes, Numerical Analysis and Applied Mathematics Icnaam 2011: International Conference on Numerical Analysis and Applied Mathematics, Vols a-C, Volume: 1389, 2011.
  11. M. Feistauer, J. Horáček, A. Kosík, V. Kučera, J. Prokopová: Simulation of Interaction of Compressible Flow with Elastic Structures with Applications to Vibrations of Human Vocal Folds, Numerical Analysis and Applied Mathematics Icnaam 2011: International Conference on Numerical Analysis and Applied Mathematics, Vols a-C, Volume: 1389, 2011.
  12. M. Feistauer, V. Kučera, K. Najzar and J. Prokopová: Space-time DG method for nonstationary convection-diffusion problems, Proc. of the conf. ENUMATH 2009, G. Kreiss, P. Lotstedt, A. Malqvist, M. Neytcheva, Editors. Springer, Heidelberg, 325-334, 2010.
  13. V. Kučera: Optimal error estimates in the DG method for nonlinear convection-diffusion problems, Algoritmy 2009: 18th Conference on Scientific Computing, 236-245, 2009.
  14. M. Feistauer, V. Kučera, J. Prokopová: ALE discontinuous Galerkin simulation of compressible flow in time dependent domains, Flow-Induced Vibration, 73-77, 2008
  15. M. Feistauer, V. Kučera: A new technique for the numerical solution of the compressible Euler equations with arbitrary Mach numbers. Hyperbolic Problems: Theory, Numerics, Applications, 523-531, 2008.

Books, course materials, etc.

  1. V. Kučera: Numerical methods for nonlinear equations. Available online.
  2. M. Feistauer, V. Kučera: Základy numerické matematiky. MatfyzPress, Charles University in Prague, 2014.
  3. V. Dolejší, P. Knobloch, V. Kučera, V. Vlasák: Finite element methods: theory, applications and implementations. MatfyzPress, Charles University in Prague, 2013.