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A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations

Sarah Ali Hassan , Caroline Japhet , Michel Kern , Martin Vohralík
Computational Methods in Applied Mathematics, 2018, 18 (3), pp.495-519. ⟨10.1515/cmam-2018-0010⟩
Article dans une revue hal-01529532v3
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Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
Comptes Rendus. Mathématique, 2020, 358 (9-10), pp.1101-1110. ⟨10.5802/crmath.133⟩
Article dans une revue hal-02631319v1
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Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling

Gergina Pencheva , Martin Vohralík , Mary Wheeler , Tim Wildey
SIAM Journal on Numerical Analysis, 2013, 51 (1), pp.526-554. ⟨10.1137/110839047⟩
Article dans une revue hal-00467738v2
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Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem

Martin Čermák , Frédéric Hecht , Zuqi Tang , Martin Vohralík
Numerische Mathematik, 2018, 138 (4), pp.1027-1065. ⟨10.1007/s00211-017-0925-3⟩
Article dans une revue hal-01097662v4
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Adaptive inexact Newton methods for discretizations of nonlinear diffusion PDEs. II. Applications

Alexandre Ern , Martin Vohralík
2012
Rapport hal-00681426v1
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Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal $hp$ approximation estimates in $H$(div)

Alexandre Ern , Thirupathi Gudi , Iain Smears , Martin Vohralík
IMA Journal of Numerical Analysis, 2022, 42 (2), pp.1023-1049. ⟨10.1093/imanum/draa103⟩
Article dans une revue hal-02268960v4
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Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations

Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík
SIAM Journal on Numerical Analysis, 2017, 55 (5), pp.2228-2254. ⟨10.1137/15M1038633⟩
Article dans une revue hal-01194364v3
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A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations

Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík
Comptes Rendus. Mathématique, 2014, 352 (11), pp.941-946. ⟨10.1016/j.crma.2014.09.014⟩
Article dans une revue hal-00994568v1
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Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the De Rham complex

Théophile Chaumont-Frelet , Martin Vohralík
2023
Pré-publication, Document de travail hal-03749682v1
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Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality

Ibtihel Ben Gharbia , Joëlle Ferzly , Martin Vohralík , Soleiman Yousef
Computers & Mathematics with Applications, 2023, 133, pp.12-29. ⟨10.1016/j.camwa.2022.11.031⟩
Article dans une revue hal-03696024v2
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Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems

Alexandre Ern , Annette Stephansen , Martin Vohralík
Journal of Computational and Applied Mathematics, 2009, 234 (1), pp.114-130. ⟨10.1016/j.cam.2009.12.009⟩
Article dans une revue hal-00193540v3
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Guaranteed contraction of adaptive inexact $hp$-refinement strategies with realistic stopping criteria

Patrik Daniel , Martin Vohralík
ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (1), pp.329 - 366. ⟨10.1051/m2an/2022082⟩
Article dans une revue hal-02486433v3
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A perturbation-method-based post-processing for the planewave discretization of Kohn–Sham models

Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík
Journal of Computational Physics, 2016, 307, pp.446-459. ⟨10.1016/j.jcp.2015.12.012⟩
Article dans une revue hal-01140818v2
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Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework

Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík
Numerische Mathematik, 2018, 140 (4), pp.1033-1079. ⟨10.1007/s00211-018-0984-0⟩
Article dans une revue hal-01483461v3
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$hp$-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems

Vít Dolejší , Alexandre Ern , Martin Vohralík
SIAM Journal on Scientific Computing, 2016, 38 (5), pp.A3220-A3246. ⟨10.1137/15M1026687⟩
Article dans une revue hal-01165187v3
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Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters

Eric Cancès , Geneviève Dusson , Yvon Maday , Benjamin Stamm , Martin Vohralík
Mathematics of Computation, 2020, 89 (326), pp.2563-2611. ⟨10.1090/mcom/3549⟩
Article dans une revue hal-02127954v3
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Sharp algebraic and total a posteriori error bounds for $h$ and $p$ finite elements via a multilevel approach. Recovering mass balance in any situation

Jan Papež , Ulrich Rüde , Martin Vohralík , Barbara I Wohlmuth
Computer Methods in Applied Mechanics and Engineering, 2020, 371, pp.113243. ⟨10.1016/j.cma.2020.113243⟩
Article dans une revue hal-01662944v5
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Four closely related equilibrated flux reconstructions for nonconforming finite elements

Alexandre Ern , Martin Vohralík
Comptes Rendus. Mathématique, 2013, 351 (1-2), pp.77-80. ⟨10.1016/j.crma.2013.01.001⟩
Article dans une revue hal-00750777v1
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Adaptive regularization for the Richards equation

François Févotte , Ari Rappaport , Martin Vohralík
2023
Pré-publication, Document de travail hal-04266827v1
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Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs

Alexandre Ern , Martin Vohralík
SIAM Journal on Scientific Computing, 2013, 35 (4), pp.A1761-A1791. ⟨10.1137/120896918⟩
Article dans une revue hal-00681422v2
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Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions

Alexandre Ern , Martin Vohralík
Mathematics of Computation, 2020, 89 (322), pp.551-594. ⟨10.1090/mcom/3482⟩
Article dans une revue hal-01422204v4
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A-posteriori-steered $p$-robust multigrid with optimal step-sizes and adaptive number of smoothing steps

Ani Miraçi , Jan Papež , Martin Vohralík
SIAM Journal on Scientific Computing, 2021, Special Section: 2020 Copper Mountain Conference, 43 (5), pp.S117-S145. ⟨10.1137/20M1349503⟩
Article dans une revue hal-02494538v5
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$p$-robust equivalence of global continuous and local discontinuous approximation, a $p$-stable local projector, and optimal elementwise $hp$ approximation estimates in $H^1$

Martin Vohralík
2024
Pré-publication, Document de travail hal-04436063v1
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An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow

Clément Cancès , Iuliu Sorin Pop , Martin Vohralík
Mathematics of Computation, 2014, 83 (285), pp.153-188. ⟨10.1090/S0025-5718-2013-02723-8⟩
Article dans une revue hal-00623209v2
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A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media

Daniele Antonio Di Pietro , Eric Flauraud , Martin Vohralík , Soleiman Yousef
Journal of Computational Physics, 2014, 276, pp.163-187. ⟨10.1016/j.jcp.2014.06.061⟩
Article dans une revue hal-00839487v2
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Polynomial-degree-robust a posteriori error estimation for Maxwell's equations

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
WCCM & ECCOMAS Congress 2020 - 14th World Congress in Computational Mechanics and ECCOMAS Congress, Jan 2021, Paris, France
Communication dans un congrès hal-03403840v1

An integrated adaptive Finite Element Method

Kenan Kergrene , Alexandre Ern , Martin Vohralík , Jan Papez , Ani Miraci
14th World Congress on Computational Mechanics, WCCM-ECCOMAS, Jan 2021, Paris, France
Communication dans un congrès hal-04388994v1
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Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

Alexander Haberl , Dirk Praetorius , Stefan Schimanko , Martin Vohralík
Numerische Mathematik, 2021, 147 (3), pp.679-725. ⟨10.1007/s00211-021-01176-w⟩
Article dans une revue hal-02557718v2
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A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations

Sarah Ali Hassan , Caroline Japhet , Martin Vohralík
Electronic Transactions on Numerical Analysis, 2018, 49, pp.151-181,. ⟨10.1553/etna_vol49s151⟩
Article dans une revue hal-01586862v3
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Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

Ibrahim Cheddadi , Radek Fučík , Mariana Prieto , Martin Vohralík
ESAIM: Mathematical Modelling and Numerical Analysis, 2009, 43 (5), pp.867-888. ⟨10.1051/m2an/2009012⟩
Article dans une revue hal-00271527v1