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MAIN PUBLICATIONS

MONOGRAPHS

V. Dolejsi, G. May: Anisotropic hp-Mesh Adaptation Methods Theory, implementation and applications, Birkhauser, 2022. link

V. Dolejsi, M. Feistauer: Discontinuous Galerkin Method - Analysis and Applications to Compressible Flow, Springer-Verlag, 2015. link

PAPERS

2025

S. Congreve, V. Dolejší, S. Sakić: Error analysis for local discontinuous Galerkin semidiscretization of Richards’ equation, IMA Journal of Numerical Analysis 45 580-630, 2025 article

2024

V. Dolejší: Non-Hydrostatic Mesoscale Atmospheric Modeling by the Anisotropic Mesh Adaptive Discontinuous Galerkin Method, International Journal of Computational Fluid Dynamics, 38 (2-3): 81-101, 2024 article

V. Dolejší, H.G. Shin, M. Vlasák: Error Estimates and Adaptivity of the Space-Time Discontinuous Galerkin Method for Solving the Richards Equation. J Sci Comput 101, 11, 2024 article

2023

V. Dolejší, S. Congreve: Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors, J. Comput. Appl. Math 427(3), 115134, 2023 article

V. Dolejsi, G. May: An anisotropic hp-mesh adaptation method for time-dependent problems based on interpolation error control, J. Sci. Comput. 95, 36, 2023 article

2022

V. Dolejší, F. Roskovec: Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations. Commun. Appl. Math. Comput. 4:143-179, 2022 article

2021

V. Dolejší, F. Roskovec, M. Vlasák: A Posteriori Error Estimates for Higher Order Space-Time Galerkin Discretizations of Nonlinear Parabolic Problems, SIAM J. Numer. Anal. 59(3), 1486–1509, 2021 article

V. Dolejsi, O. Bartos, F. Roskovec: Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors, Computers and Mathematics with Applications 93: 178-198, 2021 article

V. Dolejsi, M. Svard: Numerical study of two models for viscous compressible fluid flows, J. Comput. Phys. 427: 110068, 2021 article

V. Dolejsi, M. Kuraz, P. Solin: Numerical simulation of a single ring infiltration experiment with hp-adaptive space-time discontinuous Galerkin method, Acta Polytechnica, 61(Special Issue), pp. 59–67, 2021 article

2020

A. Rangarajan, G. May, V. Dolejsi: Adjoint-based anisotropic hp-adaptation for discontinuous Galerkin methods using a continuous mesh model, J. Comput. Phys. 409:109321, 2020 article

V. Dolejsi, P. Tichy: On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates, J. Sci. Comput. 83 5, 2020 article

2019

V. Dolejsi, G. May, A. Rangarajan, F. Roskovec: A goal-oriented high-order anisotropic mesh adaptation discontinuous Galerkin method for linear convection-diffusion-reaction problems, SIAM J. Sci. Comput. 41(3):A1899-A1922, 2019. article

O. Bartos, V. Dolejsi, G. May, A. Rangarajan, F. Roskovec: A goal-oriented anisotropic hp-mesh adaptation method for linear convection-diffusion-reaction problems, Computers & Mathematics with Applications, 78(9): 2973-2993, 2019 article

E. Bezchlebova, V. Dolejsi, M. Feistauer, P. Svacek: Numerical simulation of two-phase flow of immiscible fluids by the finite element, discontinuous Galerkin and level-set methods, Advances in Computational Mathematematics 45(4):1993-2018, 2019. article

V. Dolejsi, J. Felcman, P. Kubera: FV-DG method for the pedestrian flow problem, Comput. Fluids 183:1-15, 2019 article

V. Dolejsi, M. Kuraz, P. Solin: Adaptive higher-order space-time discontinuous Galerkin method for the computer simulation of variably-saturated porous media flows, Applied Mathematical Modelling 72:276-305, 2019 article

2018

V. Dolejsi, G. May, A. Rangarajan: A continuous hp-mesh model for adaptive discontinuous Galerkin schemes Appl. Numer. Math., 124:1-24, 2018. article

A. Rangarajan, A. Chakraborty, V. Dolejsi, G. May: A continuous-mesh optimization technique for piecewise polynomial approximation on tetrahedral grids, AIAA paper 2018-3246, 2018. article

2017

V. Dolejsi, F. Roskovec: Goal-oriented error estimates including algebraic errors in discontinuous Galerkin discretizations of linear boundary value problems, Applications of Mathematics 62(6):579-605, 2017 article

V. Dolejsi, G. May, F. Roskovec, P. Solin: Anisotropic hp-mesh optimization technique based on the continuous mesh and error models, Comput. Math. Appl., 74:45-63, 2017. preprint article

A. Rangarajan, G. May, V. Dolejsi: Adjoint-based anisotropic mesh adaptation for discontinuous Galerkin methods using a continuous mesh model, AIAA paper 2017-3100, 2017 article

2016

V. Dolejsi, P. Solin: hp-discontinuous Galerkin method based on local higher order reconstruction, Appl. Math. Comput. 279:219-235, 2016. preprint article

E. Bezchlebova, V. Dolejsi, M. Feistauer: Discontinuous Galerkin method for the solution of a transport level-set problem, Comput. Math. Appl. 72(3):455-480, 2016. article

V. Dolejsi, A. Ern and M. Vohralik: hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems, SIAM J. Sci. Comput. 38(5):A3220-A3246, 2016. preprint article

2015

V. Dolejsi: Anisotropic hp-adaptive method based on interpolation error estimates in the H1-seminorm Applications of Mathematics 60(6):697-616, 2015 preprint article

V. Dolejsi: Anisotropic hp-adaptive discontinuous Galerkin method for the numerical solution of time dependent PDEs, Appl. Math. Comput., 267:682-697, 2015 preprint article

V. Dolejsi, F. Roskovec and M. Vlasak: Residual based error estimates for the space-time discontinuous Galerkin method applied to the compressible flows, Comput. Fluids 117:404-324, 2015 preprint article

V. Dolejsi, I. Sebestova, M. Vohralik: Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids, J. Sci. Comput., 64(1): 1-34, 2015 preprint article

2014

V. Dolejsi: Anisotropic hp-adaptive method based on interpolation error estimates in the Lq-norm, Appl. Numer. Math., 82: 80-114, 2014 preprint article

2013

V. Dolejsi: hp-DGFEM for nonlinear convection-diffusion problems, Math. Comput. Simul. 87:87-118, 2013. preprint article

V. Dolejsi, A. Ern and M. Vohralik: A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems, SIAM J. Numer. Anal., 51(2): 773-793, 2013. preprint article

V. Dolejsi: A design of residual error estimates for a high order BDF-DGFE method applied to compressible flows, Int. J. Numer. Methods Fluids 73(6):523-559, 2013 preprint article

2012

2011

V. Dolejsi, M. Holik, J. Hozman: Efficient solution strategy for the semi-implicit discontinuous Galerkin discretization of the Navier-Stokes equations, J. Comput. Phys. 230(11): 4176-4200, 2011.

M. Vlasak, V. Dolejsi, J. Hajek: A priori error estimates of extrapolated space-time discontinuous Galerkin method for nonlinear convection-diffusion problem, Numer. Meth. Partial Diff. Eqs., 27(6):1456-1482, 2011

2010

V. Dolejsi, O. Havle: The $L^2$-optimality of the IIPG method for odd degrees of polynomial approximation in 1D, J. Sci. Comput., 42(1):122-143, 2010.

V. Dolejsi, H.-G. Roos: BDF-FEM for parabolic singularly perturbed problems with exponential layers on layer-adapted meshes in space. Neural Parallel Sci. Comput. 18(2): 221-235, 2010

2009

M. Feistuaer, V. Dolejsi, V. Kucera, V. Sobotikova: $L^{\infty}(L^2)$-error estimates for the DGFEM applied to convection-diffusion problems on nonconforming meshes, J. Numer. Math., 17(1):45-65, 2009.

2008

V. Dolejsi, P. Kus: Adaptive backward difference formula - Discontinuous Galerkin finite element method for the solution of conservation laws, Int. J. Numer. Meth. Engng. 73(12): 1739-1766, 2008 pdf file

V. Dolejsi, M. Feistauer, V. Kucera, V. Sobotikova: An optimal L{infty}(L2) -error estimate for the discontinuous Galerkin approximation of a nonlinear non-stationary convection-diffusion problem, IMA J. Numer. Anal. 28 (3):496-521, 2008 pdf file

V. Dolejsi, T. Gallouet: A numerical solution of particular nonconservative hyperbolic problem, Comput. Fluids 37:1077-1091, 2008 pdf file

V. Dolejsi: Analysis and application of IIPG method to quasilinear nonstationary convection-diffusion problems, J. Comp. Appl. Math. 222:251-273, 2008 article

V. Dolejsi: Semi-implicit Interior Penalty Discontinuous Galerkin Met hods for Viscous Compressible Flows, Commun. Comput. Phys. 4(2): 231-274, 2008 pdf file

V. Dolejsi, M. Vlasak: Analysis of a BDF - DGFE scheme for nonlinear convection-diffusion problems, Numer. Math., 110:405-447, 2008 pdf file

2007

V. Dolejsi, M. Feistauer, J. Hozman: Analysis of semi-implicit DGFEM for nonlinear convection-diffusion problems on non-conforming meshes, Comput. Methods Appl. Mech. Engrg., 196 2813-2827, 2007 pdf file

2006

M. Breuss, V. Dolejsi and A. Meister. On an adaptive method for heat conduction problems with boundary layers, ZAMM 86 (6), 450-463, 2006. pdf file

2005

V. Dolejsi, M. Feistauer, V. Sobotikova: Analysis of the Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems Comput. Methods Appl. Mech. Eng. 194: 2709-2733, 2005. ps file

V. Dolejsi, M. Feistauer: Error estimates of the discontinuous Galerkin method for nonlinear nonstationary convection-diffusion problems 26(3): 349-383, 2005. ps file

2004

V. Dolejsi: On the Discontinuous Galerkin Method for the Numerical Solution of the Euler and the Navier-Stokes Equations Int. J. Numer. Methods Fluids 45: 1083--1106, 2004. pdf file

V. Dolejsi, M. Feistauer: A Semi-Implicit Discontinuous Galerkin Finite Element Method for the Numerical Solution of Inviscid Compressible Flow, J. Comp. Phys. 198(2): 727-746, 2004. pdf file

2003

V. Dolejsi, M. Feistauer, C. Schwab: On some aspects of the Discontinuous Galerkin finite element method for conservation laws Mathematics and Computers in Simulation 61: 333--346, 2003 ps file

V. Dolejsi, M. Feistauer: On the Discontinuous Galerkin Method for the Numerical Solution of Compressible High-Speed Flow Proceeding of ENUMATH'01 conference, In F. Brezzi, A. Buffa, S. Corsaro, A. Murli (eds): Numerical Mathematics and Advanced Applications, ENUMATH 2001, pages 65-84, Springer-Verlag, Italia, 2003. ps file

2002

V. Dolejsi, M. Feistauer, C. Schwab: On Discontinuous Galerkin Methods for Nonlinear Convection-Diffusion Problems and Compressible Flow Mathematica Bohemica, 127(2):163-179, 2002. ps file

V. Dolejsi, M. Feistauer, C. Schwab: A Finite Volume Discontinuous Galerkin Scheme for Nonlinear Convection-Diffusion Problems Calcolo 39 : 1-40, 2002. ps file

V. Dolejsi, M.Feistauer, J. Felcman: Algebraic turbulence models for unstructured meshes (unpublished) ps file

2001

V. Dolejsi: Anisotropic Mesh Adaptation Technique for Viscous Flow Simulation East-West Journal of Numerical Mathematics, 9(1):1-24,2001. ps file

1998

V. Dolejsi: Anisotropic mesh adaptation for finite volume and finite element methods on triangular meshes, Computing and Visualisation in Science, 1:165-178, 1998. ps filee

P. Angot, V. Dolejsi, M.Feistauer, J. Felcman: Analysis of a Combined Barycentric Finite Volume - Nonconforming Finite Element Method for Nonlinear Convection - Diffusion Problems, Aplications of Mathematics, 43(4):263-310, 1998. ps file

J. Felcman and V. Dolejsi: Investigation of order of accuracy for higher order schemes for finite volumes method on triangular meshes, Journal of Engineering Mechanics, 5: 327-337, 1998. ps file

1996

M.Feistauer, J. Felcman, V. Dolejsi: Numerical Simulation of Compressible Viscous Flow through Cascades of Profiles ZAMM, 76:301-304, 1996. ps file

THESIS

V. Dolejsi: Anisotropic mesh adaptation method for compressible flow, part of the habilitation thesis, 2003, ps file

V. Dolejsi: Adaptive higher order methods for compressible flow , Habilitation Thesis, Charles University Prague, 2003. ps file

V. Dolejsi: Combined finite volume - finite element methods for compressible flow on unstructured meshes Doctoral Thesis, Charles University Prague, 1998. ps file