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2020 – today
- 2024
[i14]Ani Miraçi, Jan Papez, Martin Vohralík, Ivan Yotov:
A-posteriori-steered p-robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems. CoRR abs/2406.09872 (2024)- 2023
- [j44]Ibtihel Ben Gharbia, Joëlle Ferzly
, Martin Vohralík, Soleiman Yousef:
Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality. Comput. Math. Appl. 133: 12-29 (2023) - [j43]Ibtihel Ben Gharbia, Joëlle Ferzly, Martin Vohralík, Soleiman Yousef:
Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: Adaptivity and inexact resolution. J. Comput. Appl. Math. 420: 114765 (2023) - [j42]K. Mitra, Martin Vohralík:
A posteriori error estimates for the Richards equation. Math. Comput. 93(347): 1053-1096 (2023) - [j41]Manu Jayadharan, Michel Kern, Martin Vohralík, Ivan Yotov:
A Space-Time Multiscale Mortar Mixed Finite Element Method for Parabolic Equations. SIAM J. Numer. Anal. 61(2): 675-706 (2023) - [j40]Théophile Chaumont-Frelet, Martin Vohralík:
\(p\) -Robust Equilibrated Flux Reconstruction in \(\boldsymbol{H}(\textrm{curl})\) Based on Local Minimizations: Application to a Posteriori Analysis of the Curl-Curl Problem. SIAM J. Numer. Anal. 61(4): 1783-1818 (2023) - [i13]Annalisa Buffa, Ondine Chanon, Denise Grappein, Rafael Vázquez Hernández, Martin Vohralík:
An equilibrated flux a posteriori error estimator for defeaturing problems. CoRR abs/2312.15968 (2023) - 2022
- [j39]Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík:
Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem. Math. Comput. 91(333): 37-74 (2022) - [j38]Jan Papez, Martin Vohralík:
Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations. Numer. Algorithms 89(1): 371-407 (2022) - [i12]Théophile Chaumont-Frelet, Martin Vohralík:
Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex. CoRR abs/2208.05870 (2022) - [i11]Gregor Gantner, Martin Vohralík:
Inexpensive polynomial-degree- and number-of-hanging-nodes-robust equilibrated flux a posteriori estimates for isogeometric analysis. CoRR abs/2210.08854 (2022) - [i10]Théophile Chaumont-Frelet, Martin Vohralík:
A stable local commuting projector and optimal hp approximation estimates in H(curl). CoRR abs/2210.09701 (2022) - 2021
- [j37]Ani Miraçi, Jan Papez, Martin Vohralík:
Contractive Local Adaptive Smoothing Based on Dörfler's Marking in A-Posteriori-Steered p-Robust Multigrid Solvers. Comput. Methods Appl. Math. 21(2): 445-468 (2021) - [j36]Clément Cancès, Flore Nabet, Martin Vohralík:
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. Math. Comput. 90(328): 517-563 (2021) - [j35]Alexander Haberl, Dirk Praetorius, Stefan Schimanko, Martin Vohralík:
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Numerische Mathematik 147(3): 679-725 (2021) - [j34]Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík:
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. Numerische Mathematik 148(3): 525-573 (2021) - [j33]Ani Miraçi, Jan Papez, Martin Vohralík:
A-Posteriori-Steered p-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps. SIAM J. Sci. Comput. 43(5): S117-S145 (2021) - [i9]Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík:
On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. CoRR abs/2105.01376 (2021) - [i8]Théophile Chaumont-Frelet, Martin Vohralík:
$p$-robust equilibrated flux reconstruction in ${\boldsymbol H}(\mathrm{curl})$ based on local minimizations. Application to a posteriori analysis of the curl-curl problem. CoRR abs/2105.07770 (2021) - [i7]K. Mitra, Martin Vohralík:
A posteriori error estimates for the Richards equation. CoRR abs/2108.12507 (2021) - [i6]Manu Jayadharan, Michel Kern, Martin Vohralík, Ivan Yotov:
A space-time multiscale mortar mixed finite element method for parabolic equations. CoRR abs/2110.02132 (2021) - 2020
- [j32]Gouranga Mallik, Martin Vohralík, Soleiman Yousef:
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. J. Comput. Appl. Math. 366 (2020) - [j31]Jad Dabaghi, Vincent Martin, Martin Vohralík:
Adaptive Inexact Semismooth Newton Methods for the Contact Problem Between Two Membranes. J. Sci. Comput. 84(2): 28 (2020) - [j30]Alexandre Ern, Martin Vohralík:
Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Math. Comput. 89(322): 551-594 (2020) - [j29]Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík:
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters. Math. Comput. 89(326): 2563-2611 (2020) - [j28]Ani Miraçi, Jan Papez, Martin Vohralík:
A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with p-Robust Behavior. SIAM J. Numer. Anal. 58(5): 2856-2884 (2020) - [i5]Alexander Haberl, Dirk Praetorius, Stefan Schimanko, Martin Vohralík:
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. CoRR abs/2004.13137 (2020) - [i4]Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík:
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. CoRR abs/2005.14528 (2020) - [i3]Théophile Chaumont-Frelet, Alexandre Ern, Martin Vohralík:
Stable broken H(curl) polynomial extensions and p-robust quasi-equilibrated a posteriori estimators for Maxwell's equations. CoRR abs/2005.14537 (2020) - [i2]Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík:
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters. CoRR abs/2008.04140 (2020)
2010 – 2019
- 2019
- [i1]Alexandre Ern, Thirupathi Gudi, Iain Smears, Martin Vohralík:
Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). CoRR abs/1908.08158 (2019) - 2018
- [j27]Patrik Daniel, Alexandre Ern, Iain Smears, Martin Vohralík:
An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. Comput. Math. Appl. 76(5): 967-983 (2018) - [j26]Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin Vohralík:
A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations. Comput. Methods Appl. Math. 18(3): 495-519 (2018) - [j25]Jan Papez, Zdenek Strakos, Martin Vohralík:
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Numerische Mathematik 138(3): 681-721 (2018) - [j24]Martin Cermák, Frédéric Hecht, Zuqi Tang, Martin Vohralík:
Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem. Numerische Mathematik 138(4): 1027-1065 (2018) - [j23]Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík:
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. Numerische Mathematik 140(4): 1033-1079 (2018) - 2017
- [j22]Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík:
Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations. SIAM J. Numer. Anal. 55(5): 2228-2254 (2017) - [j21]Alexandre Ern, Iain Smears, Martin Vohralík:
Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems. SIAM J. Numer. Anal. 55(6): 2811-2834 (2017) - 2016
- [j20]Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin Vohralík:
A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models. J. Comput. Phys. 307: 446-459 (2016) - [j19]Vít Dolejsí, Alexandre Ern, Martin Vohralík:
hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems. SIAM J. Sci. Comput. 38(5) (2016) - 2015
- [j18]Vít Dolejsí, Ivana Sebestová, Martin Vohralík:
Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids. J. Sci. Comput. 64(1): 1-34 (2015) - [j17]Daniele A. Di Pietro, Martin Vohralík, Soleiman Yousef:
Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. Math. Comput. 84(291): 153-186 (2015) - [j16]Alexandre Ern, Martin Vohralík:
Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations. SIAM J. Numer. Anal. 53(2): 1058-1081 (2015) - 2014
- [j15]Daniele A. Di Pietro, Martin Vohralík, Soleiman Yousef:
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. Comput. Math. Appl. 68(12): 2331-2347 (2014) - [j14]Daniele A. Di Pietro, Eric Flauraud, Martin Vohralík, Soleiman Yousef:
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. J. Comput. Phys. 276: 163-187 (2014) - [j13]Clément Cancès, Iuliu Sorin Pop, Martin Vohralík:
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. Math. Comput. 83(285): 153-188 (2014) - 2013
- [j12]Gergina Pencheva, Martin Vohralík, Mary F. Wheeler, Tim Wildey:
Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling. SIAM J. Numer. Anal. 51(1): 526-554 (2013) - [j11]Vít Dolejsí, Alexandre Ern, Martin Vohralík:
A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems. SIAM J. Numer. Anal. 51(2): 773-793 (2013) - [j10]Alexandre Ern, Martin Vohralík:
Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs. SIAM J. Sci. Comput. 35(4) (2013) - 2012
- [j9]Antti Hannukainen, Rolf Stenberg, Martin Vohralík:
A unified framework for a posteriori error estimation for the Stokes problem. Numerische Mathematik 122(4): 725-769 (2012) - 2011
- [j8]Martin Vohralík:
Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients. J. Sci. Comput. 46(3): 397-438 (2011) - 2010
- [j7]Alexandre Ern, Annette F. Stephansen, Martin Vohralík:
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. J. Comput. Appl. Math. 234(1): 114-130 (2010) - [j6]Martin Vohralík:
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Math. Comput. 79(272): 2001-2032 (2010) - [j5]Alexandre Ern, Martin Vohralík:
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation. SIAM J. Numer. Anal. 48(1): 198-223 (2010) - [j4]Pavel Jiránek, Zdenek Strakos, Martin Vohralík:
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers. SIAM J. Sci. Comput. 32(3): 1567-1590 (2010)
2000 – 2009
- 2008
- [j3]Martin Vohralík:
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Numerische Mathematik 111(1): 121-158 (2008) - 2007
- [j2]Martin Vohralík:
A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations. SIAM J. Numer. Anal. 45(4): 1570-1599 (2007) - 2006
- [j1]Robert Eymard, Danielle Hilhorst, Martin Vohralík:
A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Numerische Mathematik 105(1): 73-131 (2006) - 2004
- [b1]Martin Vohralík:
Numerical methods for nonlinear elliptic and parabolic equations. Application to flow problems in porous and fractured media. (Méthodes numériques pour des équations elliptiques et paraboliques non linéaires. Application à des problèmes d'écoulement en milieux poreux et fracturés). University of Paris-Sud, Orsay, France, 2004 - 2002
- [c1]Jirí Maryska, Otto Severýn, Martin Vohralík:
Mixed-Hybrid FEM Discrete Fracture Network Model of the Fracture Flow. International Conference on Computational Science (3) 2002: 794-803
Coauthor Index
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