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A posteriori error estimation based on potential and flux reconstruction for the heat equation

Alexandre Ern , Martin Vohralík
SIAM Journal on Numerical Analysis, 2010, 48 (1), pp.198-223. ⟨10.1137/090759008⟩
Journal articles hal-00383692v1
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An adaptive $hp$-refinement strategy with computable guaranteed bound on the error reduction factor

Patrik Daniel , Alexandre Ern , Iain Smears , Martin Vohralík
Computers & Mathematics with Applications, 2018, 76 (5), pp.967-983. ⟨10.1016/j.camwa.2018.05.034⟩
Journal articles hal-01666763v2
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Discrete $p$-robust H(div)-liftings and a posteriori estimates for elliptic problems with $H^{-1}$ source terms

Alexandre Ern , Iain Smears , Martin Vohralík
Calcolo, 2017, 54 (3), pp.1009-1025. ⟨10.1007/s10092-017-0217-4⟩
Journal articles hal-01377007v1
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Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: Adaptivity and inexact resolution

Ibtihel Ben Gharbia , Joëlle Ferzly , Martin Vohralík , Soleiman Yousef
Journal of Computational and Applied Mathematics, 2023, 420, pp.114765. ⟨10.1016/j.cam.2022.114765⟩
Journal articles hal-03355116v2
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A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems

Vít Dolejší , Alexandre Ern , Martin Vohralík
SIAM Journal on Numerical Analysis, 2013, 51 (2), pp.773-793. ⟨10.1137/110859282⟩
Journal articles hal-00652979v2
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A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences

Daniele Antonio Di Pietro , Martin Vohralík
Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, 2014, 69 (4), pp.701-730. ⟨10.2516/ogst/2013158⟩
Journal articles hal-00783068v1
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Polynomial-degree-robust a posteriori error estimation for Maxwell's equations

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
ICOSAHOM 2021 - International Conference on Spectral High Order Methods, Jul 2021, Vienna, Austria
Conference papers hal-03403944v1
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A stable local commuting projector and optimal hp approximation estimates in H(curl)

Théophile Chaumont-Frelet , Martin Vohralík
2022
Preprints, Working Papers, ... hal-03817302v1
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Equivalence of local-best and global-best approximations in H(curl)

Théophile Chaumont-Frelet , Martin Vohralík
Calcolo, 2021, 58, pp.53. ⟨10.1007/s10092-021-00430-9⟩
Journal articles hal-02736200v2
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A multilevel algebraic error estimator and the corresponding iterative solver with $p$-robust behavior

Ani Miraçi , Jan Papež , Martin Vohralík
SIAM Journal on Numerical Analysis, 2020, 58 (5), pp.2856-2884. ⟨10.1137/19M1275929⟩
Journal articles hal-02070981v5
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Mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods

Martin Vohralík , Barbara Wohlmuth
Mathematical Models and Methods in Applied Sciences, 2013, 23 (5), pp.803-838. ⟨10.1142/S0218202512500613⟩
Journal articles hal-00497394v3
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Guaranteed error estimates for finite element discretizations of Helmholtz problems

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
Numerical Waves, Oct 2021, Nice, France
Conference papers hal-03404014v1
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On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
Numerische Mathematik, 2021, 148 (3), pp.525-573. ⟨10.1007/s00211-021-01192-w⟩
Journal articles hal-02202233v3
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p-robust equilibrated flux reconstruction in H(curl) based on local minimizations. Application to a posteriori analysis of the curl-curl problem

Théophile Chaumont-Frelet , Martin Vohralík
SIAM Journal on Numerical Analysis, In press
Journal articles hal-03227570v2
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Asymptotically constant-free, p-robust and guaranteed a posteriori error estimates for the Helmholtz equation

Théophile Chaumont-Frelet , Alexandre Ern , Martin Vohralík
EnuMath 2019 - European Numerical Mathematics and Advanced Applications Conference, Sep 2019, Egmond aan Zee, Netherlands
Conference papers hal-02321140v1
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Localization of the $W^{-1,q}$ norm for local a posteriori efficiency

Jan Blechta , Josef Málek , Martin Vohralík
IMA Journal of Numerical Analysis, 2020, 40 (2), pp.914-950. ⟨10.1093/imanum/drz002⟩
Journal articles hal-01332481v3

Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes

Martin Vohralík
Modelisation Mathématique et Analyse Numérique (M2AN), 2006, 40, pp.367-391
Journal articles hal-00114646v1
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Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems

Alexandre Ern , Iain Smears , Martin Vohralík
SIAM Journal on Numerical Analysis, 2017, 55 (6), pp.2811-2834. ⟨10.1137/16M1097626⟩
Journal articles hal-01377086v1
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From face to element unknowns by local static condensation with application to nonconforming finite elements

Martin Vohralík , Barbara Wohlmuth
Computer Methods in Applied Mechanics and Engineering, 2013, 253, pp.517-529. ⟨10.1016/j.cma.2012.08.013⟩
Journal articles hal-00614633v2
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A unified framework for a posteriori error estimation for the Stokes problem

Antti Hannukainen , Rolf Stenberg , Martin Vohralík
Numerische Mathematik, 2012, 122 (4), pp.725-769. ⟨10.1007/s00211-012-0472-x⟩
Journal articles hal-00470131v2
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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⟩
Journal articles hal-01662944v5
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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, In press, ⟨10.1051/m2an/2022082⟩
Journal articles hal-02486433v3
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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⟩
Journal articles 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⟩
Journal articles hal-01165187v3
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Inexpensive polynomial-degree-robust equilibrated flux a posteriori estimates for isogeometric analysis

Gregor Gantner , Martin Vohralík
2023
Preprints, Working Papers, ... hal-03819048v2
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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⟩
Journal articles hal-00193540v3
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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⟩
Journal articles hal-01140818v2
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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⟩
Journal articles hal-00750777v1
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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, In press, 133, pp.12-29. ⟨10.1016/j.camwa.2022.11.031⟩
Journal articles hal-03696024v2
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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⟩
Journal articles hal-02127954v3