## Vohralík, Martin

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 Author ID: vohralik.martin Published as: Vohralík, Martin; Vohralík, M.; Vohralıḱ, Martin; VohralÍk, Martin more...less
 Documents Indexed: 89 Publications since 2001 Co-Authors: 63 Co-Authors with 78 Joint Publications 1,726 Co-Co-Authors
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### Co-Authors

 11 single-authored 20 Ern, Alexandre 6 Cancès, Eric 6 Dusson, Geneviève 6 Maday, Yvon 6 Maryška, Jiří 6 Papež, Jan 6 Severýn, Otto 6 Smears, Iain 6 Stamm, Benjamin 5 Yousef, Soleiman 4 Chaumont-Frelet, Théophile 4 Di Pietro, Daniele Antonio 4 Hassan, Sarah Ali 4 Hilhorst, Danielle 4 Japhet, Caroline 3 Ben Belgacem, Faker 3 Bernardi, Christine 3 Blouza, Adel 3 Dabaghi, Jad 3 Dolejší, Vít 3 Eymard, Robert 3 Kern, Michel 3 Martin, Vincent 3 Miraçi, Ani 3 Wohlmuth, Barbara I. 2 Cancès, Clément 2 Cheddadi, Ibrahim 2 Daniel, Patrik 2 Fučík, Radek 2 Prieto, Mariana I. 2 Strakoš, Zdeněk 2 Wheeler, Mary Fanett 1 Ahmed, Elyes 1 Ben Gharbia, Ibtihel 1 Blechta, Jan 1 Čermák, Martin 1 Chalhoub, Nancy 1 Ciarlet, Patrick jun. 1 El Alaoui, Linda 1 Ern, Alexndre 1 Flauraud, Eric 1 Gudi, Thirupathi 1 Haberl, Alexander 1 Hannukainen, Antti 1 Hecht, Frédéric 1 Jiránek, Pavel 1 Málek, Josef 1 Mallik, Gouranga 1 Nabet, Flore 1 Nicaise, Serge 1 Pencheva, Gergina V. 1 Pop, Iuliu Sorin 1 Praetorius, Dirk 1 Rüde, Ulrich 1 Sayah, Tony 1 Schimanko, Stefan 1 Šebestová, Ivana 1 Stenberg, Rolf 1 Stephansen, Annette F. 1 Tang, Zuqi 1 Widmer, Carole 1 Wildey, Tim M. 1 Zakerzadeh, Mohammad Reza
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### Serials

 8 Numerische Mathematik 8 SIAM Journal on Numerical Analysis 7 Computer Methods in Applied Mechanics and Engineering 7 Mathematics of Computation 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 IMA Journal of Numerical Analysis 4 SIAM Journal on Scientific Computing 3 Journal of Scientific Computing 3 Computational Geosciences 2 Computers & Mathematics with Applications 2 Journal of Computational Physics 2 Calcolo 2 Journal of Computational and Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Computational Methods in Applied Mathematics 1 Numerical Functional Analysis and Optimization 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 ETNA. Electronic Transactions on Numerical Analysis 1 Mathematical Modelling of Natural Phenomena 1 SMAI Journal of Computational Mathematics
all top 5

### Fields

 83 Numerical analysis (65-XX) 42 Partial differential equations (35-XX) 28 Fluid mechanics (76-XX) 5 Mechanics of deformable solids (74-XX) 4 Functional analysis (46-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

79 Publications have been cited 1,145 times in 517 Documents Cited by Year
Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. Zbl 1312.76026
Ern, Alexandre; Vohralík, Martin
2015
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
2013
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. Zbl 1190.65165
Ern, Alexandre; Stephansen, Annette F.; Vohralík, Martin
2010
A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1151.65084
Vohralík, Martin
2007
A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Zbl 1108.65099
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2006
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. Zbl 1215.65168
Jiránek, Pavel; Strakoš, Zdeněk; Vohralík, Martin
2010
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Zbl 1230.65118
El Alaoui, Linda; Ern, Alexandre; Vohralík, Martin
2011
An accurate $$\mathbf H$$(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
2007
Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. Zbl 1270.65064
Vohralík, Martin
2011
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Zbl 1160.65059
Vohralík, Martin
2008
A unified framework for a posteriori error estimation for the Stokes problem. Zbl 1301.76049
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin
2012
On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space $$H^1$$. Zbl 1089.65124
Vohralík, Martin
2005
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Zbl 1201.65200
Vohralík, Martin
2010
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems. Zbl 1190.65164
Cheddadi, Ibrahim; Fučík, Radek; Prieto, Mariana I.; Vohralík, Martin
2009
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
2010
Mixed finite element methods: Implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods. Zbl 1264.65198
Vohralík, Martin; Wohlmuth, Barbara I.
2013
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. Zbl 1430.76369
Cancès, Clément; Pop, Iuliu Sorin; Vohralík, Martin
2014
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2013
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Zbl 1393.76069
Vohralík, Martin; Wheeler, Mary F.
2013
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. Zbl 1116.65121
Vohralík, Martin
2006
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. Zbl 1349.76323
Di Pietro, Daniele A.; Flauraud, Eric; Vohralík, Martin; Yousef, Soleiman
2014
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
2009
Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling. Zbl 1267.65165
Pencheva, Gergina V.; Vohralík, Martin; Wheeler, Mary F.; Wildey, Tim
2013
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Zbl 1453.65414
Papež, J.; Strakoš, Z.; Vohralík, M.
2018
$$hp$$-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2016
A combined finite volume-finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids. Zbl 1192.65117
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2010
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations. Zbl 06779777
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2017
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. Zbl 1378.65165
Ern, Alexandre; Smears, Iain; VohralÍk, Martin
2017
A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. Zbl 1142.65086
Vohralík, Martin
2008
Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Zbl 1116.76427
Maryška, Jiří; Severýn, Otto; Vohralík, Martin
2004
Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. Zbl 1307.65123
Di Pietro, Daniele A.; Vohralík, Martin; Yousef, Soleiman
2015
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 1490.65282
Mallik, Gouranga; Vohralík, Martin; Yousef, Soleiman
2020
Stable broken $$H^1$$ and $$H(\operatorname{div})$$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Zbl 1434.65253
Ern, Alexandre; Vohralík, Martin
2020
Mixed and nonconforming finite element methods on a system of polygons. Zbl 1112.65123
Vohralík, M.; Maryška, J.; Severýn, O.
2007
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
2013
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. Zbl 1362.65097
Di Pietro, Daniele A.; Vohralík, Martin; Yousef, Soleiman
2014
Computable a posteriori error estimates in the finite element method based on its local conservativity: improvements using local minimization. Zbl 1156.65318
Cheddadi, Ibrahim; Fučík, Radek; Prieto, Mariana I.; Vohralík, Martin
2008
Discrete $$p$$-robust $$\boldsymbol H(\mathrm{div})$$-liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ source terms. Zbl 1378.65173
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2017
Two types of guaranteed (and robust) a posteriori estimates for finite volume methods. Zbl 1422.65346
Vohralík, Martin
2008
On the unilateral contact between membranes. II: A posteriori analysis and numerical experiments. Zbl 1451.74176
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
2012
A posteriori error estimates for combined finite volume-finite element discretizations of reactive transport equations on nonmatching grids. Zbl 1225.76212
Hilhorst, Danielle; Vohralík, Martin
2011
Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. Zbl 1417.65187
Ciarlet Jr., Patrick; Vohralík, Martin
2018
A finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
2009
On the unilateral contact between membranes. I: Finite element discretization and mixed reformulation. Zbl 1162.74031
Ben Belgacem, F.; Bernardi, C.; Blouza, A.; Vohralík, M.
2009
A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations. Zbl 1398.65272
Hassan, Sarah Ali; Japhet, Caroline; Kern, Michel; Vohralík, Martin
2018
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. Zbl 1402.65137
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2018
Localization of the $$W^{-1,q}$$ norm for local a posteriori efficiency. Zbl 07199497
Blechta, Jan; Málek, Josef; Vohralík, Martin
2020
A multilevel algebraic error estimator and the corresponding iterative solver with $$p$$-robust behavior. Zbl 1451.65222
Miraçi, Ani; Papež, Jan; Vohralík, Martin
2020
A unified framework for a posteriori error estimation in elliptic and parabolic problems with application to finite volumes. Zbl 1246.65162
Ern, Alexandre; Vohralıḱ, Martin
2011
A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations. (Un estimateur d’erreur a posteriori basé sur une méthode de perturbation pour la discrétisation des équations de Schrödinger non linéaires dans une base d’ondes planes.) Zbl 1303.65077
Cancès, Éric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2014
From face to element unknowns by local static condensation with application to nonconforming finite elements. Zbl 1297.65163
Vohralík, Martin; Wohlmuth, Barbara I.
2013
A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types. Zbl 1432.65130
Ahmed, Elyes; Ali Hassan, Sarah; Japhet, Caroline; Kern, Michel; Vohralík, Martin
2019
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
2018
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters. Zbl 1446.35083
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2020
Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids. Zbl 1326.65147
Dolejší, Vít; Šebestová, Ivana; Vohralík, Martin
2015
A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations. Zbl 1397.65167
Hassan, Sarah Ali; Japhet, Caroline; Vohralík, Martin
2018
Adaptive inexact semismooth Newton methods for the contact problem between two membranes. Zbl 07229481
Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
2020
An adaptive $$hp$$-refinement strategy with computable guaranteed bound on the error reduction factor. Zbl 1427.65356
Daniel, Patrik; Ern, Alexandre; Smears, Iain; Vohralík, Martin
2018
Equilibrated flux a posteriori error estimates in $$L^2(H^1)$$-norms for high-order discretizations of parabolic problems. Zbl 1467.65092
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2019
Sharp algebraic and total a posteriori error bounds for $$h$$ and $$p$$ finite elements via a multilevel approach. Recovering mass balance in any situation. Zbl 07337929
Papež, Jan; Rüde, Ulrich; Vohralík, Martin; Wohlmuth, Barbara
2020
Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems. Zbl 1470.65199
Smears, Iain; Vohralík, Martin
2020
On the derivation of guaranteed and $$p$$-robust a posteriori error estimates for the Helmholtz equation. Zbl 07387428
Chaumont-Frelet, T.; Ern, A.; Vohralík, M.
2021
Equivalence between mixed finite element and multi-point finite volume methods. Zbl 1058.65132
Vohralík, Martin
2004
An a posteriori error estimator for a finite volume discretization of the two-phase flow. Zbl 1246.76079
Di Pietro, Daniele A.; Vohralík, Martin; Widmer, Carole
2011
Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem. Zbl 1448.65221
Čermák, Martin; Hecht, Frédéric; Tang, Zuqi; Vohralík, Martin
2018
An adaptive $$hp$$-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor. Zbl 1441.65095
Daniel, Patrik; Ern, Alexandre; Vohralík, Martin
2020
Polynomial-degree-robust $$\boldsymbol H(\mathbf{curl})$$-stability of discrete minimization in a tetrahedron. Zbl 1456.65156
Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin
2020
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal $$hp$$ approximation estimates in $$\boldsymbol{H}(\operatorname{div})$$. Zbl 07524708
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin
2022
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191
Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin
2021
A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models. Zbl 1352.65005
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2016
A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1359.76199
Vohralík, Martin
2007
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. Zbl 1456.65105
Cancès, Clément; Nabet, Flore; Vohralík, Martin
2021
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. Zbl 1180.65154
Vohralík, Martin
2005
Mixed-hybrid discrete fracture network model. Zbl 1041.76046
Vohralík, Martin; Maryška, Jiří; Severýn, Otto
2003
Mixed-hybrid FEM discrete fracture network model of the fracture flow. Zbl 1054.76051
Maryška, Jiří; Severý, Otto; Vohralík, Martin
2002
Combined nonconforming/mixed-hybrid finite element-finite volume scheme for degenerate parabolic problems. Zbl 1056.65078
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2004
A posteriori error estimates for unsteady convection-diffusion-reaction problems and the finite volume method. Zbl 1246.65210
Chalhoub, Nancy; Ern, Alexandre; Sayah, Tony; Vohralıḱ, Martin
2011
Space-time domain decomposition methods and a posteriori error estimates for the heat equation. Zbl 1397.65178
Japhet, C.; Hassan, S. Ali; Kern, M.; Vohralík, M.
2018
A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints. Zbl 1439.76150
Ben Gharbia, Ibtihel; Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
2020
Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal $$hp$$ approximation estimates in $$\boldsymbol{H}(\operatorname{div})$$. Zbl 07524708
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin
2022
On the derivation of guaranteed and $$p$$-robust a posteriori error estimates for the Helmholtz equation. Zbl 07387428
Chaumont-Frelet, T.; Ern, A.; Vohralík, M.
2021
Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. Zbl 1468.65191
Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin
2021
Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. Zbl 1456.65105
Cancès, Clément; Nabet, Flore; Vohralík, Martin
2021
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 1490.65282
Mallik, Gouranga; Vohralík, Martin; Yousef, Soleiman
2020
Stable broken $$H^1$$ and $$H(\operatorname{div})$$ polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. Zbl 1434.65253
Ern, Alexandre; Vohralík, Martin
2020
Localization of the $$W^{-1,q}$$ norm for local a posteriori efficiency. Zbl 07199497
Blechta, Jan; Málek, Josef; Vohralík, Martin
2020
A multilevel algebraic error estimator and the corresponding iterative solver with $$p$$-robust behavior. Zbl 1451.65222
Miraçi, Ani; Papež, Jan; Vohralík, Martin
2020
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters. Zbl 1446.35083
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2020
Adaptive inexact semismooth Newton methods for the contact problem between two membranes. Zbl 07229481
Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
2020
Sharp algebraic and total a posteriori error bounds for $$h$$ and $$p$$ finite elements via a multilevel approach. Recovering mass balance in any situation. Zbl 07337929
Papež, Jan; Rüde, Ulrich; Vohralík, Martin; Wohlmuth, Barbara
2020
Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems. Zbl 1470.65199
Smears, Iain; Vohralík, Martin
2020
An adaptive $$hp$$-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor. Zbl 1441.65095
Daniel, Patrik; Ern, Alexandre; Vohralík, Martin
2020
Polynomial-degree-robust $$\boldsymbol H(\mathbf{curl})$$-stability of discrete minimization in a tetrahedron. Zbl 1456.65156
Chaumont-Frelet, Théophile; Ern, Alexandre; Vohralík, Martin
2020
A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints. Zbl 1439.76150
Ben Gharbia, Ibtihel; Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
2020
A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types. Zbl 1432.65130
Ahmed, Elyes; Ali Hassan, Sarah; Japhet, Caroline; Kern, Michel; Vohralík, Martin
2019
Equilibrated flux a posteriori error estimates in $$L^2(H^1)$$-norms for high-order discretizations of parabolic problems. Zbl 1467.65092
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2019
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Zbl 1453.65414
Papež, J.; Strakoš, Z.; Vohralík, M.
2018
Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients. Zbl 1417.65187
Ciarlet Jr., Patrick; Vohralík, Martin
2018
A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations. Zbl 1398.65272
Hassan, Sarah Ali; Japhet, Caroline; Kern, Michel; Vohralík, Martin
2018
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. Zbl 1402.65137
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2018
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
2018
A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations. Zbl 1397.65167
Hassan, Sarah Ali; Japhet, Caroline; Vohralík, Martin
2018
An adaptive $$hp$$-refinement strategy with computable guaranteed bound on the error reduction factor. Zbl 1427.65356
Daniel, Patrik; Ern, Alexandre; Smears, Iain; Vohralík, Martin
2018
Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem. Zbl 1448.65221
Čermák, Martin; Hecht, Frédéric; Tang, Zuqi; Vohralík, Martin
2018
Space-time domain decomposition methods and a posteriori error estimates for the heat equation. Zbl 1397.65178
Japhet, C.; Hassan, S. Ali; Kern, M.; Vohralík, M.
2018
Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations. Zbl 06779777
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2017
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems. Zbl 1378.65165
Ern, Alexandre; Smears, Iain; VohralÍk, Martin
2017
Discrete $$p$$-robust $$\boldsymbol H(\mathrm{div})$$-liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ source terms. Zbl 1378.65173
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2017
$$hp$$-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2016
A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models. Zbl 1352.65005
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2016
Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. Zbl 1312.76026
Ern, Alexandre; Vohralík, Martin
2015
Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. Zbl 1307.65123
Di Pietro, Daniele A.; Vohralík, Martin; Yousef, Soleiman
2015
Algebraic and discretization error estimation by equilibrated fluxes for discontinuous Galerkin methods on nonmatching grids. Zbl 1326.65147
Dolejší, Vít; Šebestová, Ivana; Vohralík, Martin
2015
An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. Zbl 1430.76369
Cancès, Clément; Pop, Iuliu Sorin; Vohralík, Martin
2014
A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. Zbl 1349.76323
Di Pietro, Daniele A.; Flauraud, Eric; Vohralík, Martin; Yousef, Soleiman
2014
An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. Zbl 1362.65097
Di Pietro, Daniele A.; Vohralík, Martin; Yousef, Soleiman
2014
A perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations. (Un estimateur d’erreur a posteriori basé sur une méthode de perturbation pour la discrétisation des équations de Schrödinger non linéaires dans une base d’ondes planes.) Zbl 1303.65077
Cancès, Éric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2014
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
2013
Mixed finite element methods: Implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods. Zbl 1264.65198
Vohralík, Martin; Wohlmuth, Barbara I.
2013
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
2013
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Zbl 1393.76069
Vohralík, Martin; Wheeler, Mary F.
2013
Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling. Zbl 1267.65165
Pencheva, Gergina V.; Vohralík, Martin; Wheeler, Mary F.; Wildey, Tim
2013
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
2013
From face to element unknowns by local static condensation with application to nonconforming finite elements. Zbl 1297.65163
Vohralík, Martin; Wohlmuth, Barbara I.
2013
A unified framework for a posteriori error estimation for the Stokes problem. Zbl 1301.76049
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin
2012
On the unilateral contact between membranes. II: A posteriori analysis and numerical experiments. Zbl 1451.74176
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
2012
Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. Zbl 1230.65118
El Alaoui, Linda; Ern, Alexandre; Vohralík, Martin
2011
Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. Zbl 1270.65064
Vohralík, Martin
2011
A posteriori error estimates for combined finite volume-finite element discretizations of reactive transport equations on nonmatching grids. Zbl 1225.76212
Hilhorst, Danielle; Vohralík, Martin
2011
A unified framework for a posteriori error estimation in elliptic and parabolic problems with application to finite volumes. Zbl 1246.65162
Ern, Alexandre; Vohralıḱ, Martin
2011
An a posteriori error estimator for a finite volume discretization of the two-phase flow. Zbl 1246.76079
Di Pietro, Daniele A.; Vohralík, Martin; Widmer, Carole
2011
A posteriori error estimates for unsteady convection-diffusion-reaction problems and the finite volume method. Zbl 1246.65210
Chalhoub, Nancy; Ern, Alexandre; Sayah, Tony; Vohralıḱ, Martin
2011
Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. Zbl 1190.65165
Ern, Alexandre; Stephansen, Annette F.; Vohralík, Martin
2010
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. Zbl 1215.65168
Jiránek, Pavel; Strakoš, Zdeněk; Vohralík, Martin
2010
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Zbl 1201.65200
Vohralík, Martin
2010
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
2010
A combined finite volume-finite element scheme for the discretization of strongly nonlinear convection-diffusion-reaction problems on nonmatching grids. Zbl 1192.65117
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2010
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems. Zbl 1190.65164
Cheddadi, Ibrahim; Fučík, Radek; Prieto, Mariana I.; Vohralík, Martin
2009
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
2009
A finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
2009
On the unilateral contact between membranes. I: Finite element discretization and mixed reformulation. Zbl 1162.74031
Ben Belgacem, F.; Bernardi, C.; Blouza, A.; Vohralík, M.
2009
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Zbl 1160.65059
Vohralík, Martin
2008
A posteriori error estimation in the conforming finite element method based on its local conservativity and using local minimization. Zbl 1142.65086
Vohralík, Martin
2008
Computable a posteriori error estimates in the finite element method based on its local conservativity: improvements using local minimization. Zbl 1156.65318
Cheddadi, Ibrahim; Fučík, Radek; Prieto, Mariana I.; Vohralík, Martin
2008
Two types of guaranteed (and robust) a posteriori estimates for finite volume methods. Zbl 1422.65346
Vohralík, Martin
2008
A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1151.65084
Vohralík, Martin
2007
An accurate $$\mathbf H$$(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
2007
Mixed and nonconforming finite element methods on a system of polygons. Zbl 1112.65123
Vohralík, M.; Maryška, J.; Severýn, O.
2007
A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1359.76199
Vohralík, Martin
2007
A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Zbl 1108.65099
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2006
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. Zbl 1116.65121
Vohralík, Martin
2006
On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space $$H^1$$. Zbl 1089.65124
Vohralík, Martin
2005
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. Zbl 1180.65154
Vohralík, Martin
2005
Numerical simulation of fracture flow with a mixed-hybrid FEM stochastic discrete fracture network model. Zbl 1116.76427
Maryška, Jiří; Severýn, Otto; Vohralík, Martin
2004
Equivalence between mixed finite element and multi-point finite volume methods. Zbl 1058.65132
Vohralík, Martin
2004
Combined nonconforming/mixed-hybrid finite element-finite volume scheme for degenerate parabolic problems. Zbl 1056.65078
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
2004
Mixed-hybrid discrete fracture network model. Zbl 1041.76046
Vohralík, Martin; Maryška, Jiří; Severýn, Otto
2003
Mixed-hybrid FEM discrete fracture network model of the fracture flow. Zbl 1054.76051
Maryška, Jiří; Severý, Otto; Vohralík, Martin
2002
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### Cited by 735 Authors

 58 Vohralík, Martin 21 Ern, Alexandre 13 Pop, Iuliu Sorin 13 Radu, Florin Adrian 13 Wihler, Thomas Pascal 10 Di Pietro, Daniele Antonio 10 Dolejší, Vít 10 Park, Eun-Jae 9 Papež, Jan 9 Saad, Mazen 9 Zhao, Jikun 8 Chaumont-Frelet, Théophile 8 Zhang, Bei 7 Ahmed, Elyes 7 Chen, Shaochun 7 Vejchodský, Tomáš 7 Wheeler, Mary Fanett 7 Zhang, Shun 6 Ainsworth, Mark 6 Bernardi, Christine 6 Bertrand, Fleurianne 6 Cancès, Clément 6 Droniou, Jérôme 6 Georgoulis, Emmanuil H. 6 Giani, Stefano 6 Heid, Pascal 6 Kim, Kwang Yeon 6 Nicaise, Serge 6 Nordbotten, Jan Martin 6 Sayah, Toni 6 Smears, Iain 6 Zhao, Lina 5 Berrone, Stefano 5 Boffi, Daniele 5 Cai, Zhiqiang 5 Carstensen, Carsten 5 Du, Shaohong 5 Dusson, Geneviève 5 Eymard, Robert 5 He, Cuiyu 5 Japhet, Caroline 5 Langer, Ulrich 5 Maday, Yvon 5 Merdon, Christian 5 Mu, Lin 5 Quenjel, EL Houssaine 5 Roskovec, Filip 5 Stamm, Benjamin 5 Starke, Gerhard 5 Verani, Marco 5 Wick, Thomas 5 Wohlmuth, Barbara I. 5 Yousef, Soleiman 4 Achchab, Boujemaa 4 Agouzal, Abdellatif 4 Amaziane, Brahim 4 Amrein, Mario 4 Beirão da Veiga, Lourenço 4 Cancès, Eric 4 Cangiani, Andrea 4 Canuto, Claudio 4 Creusé, Emmanuel 4 Dabaghi, Jad 4 Endtmayer, Bernhard 4 Erath, Christoph 4 Gedicke, Joscha 4 Hilhorst, Danielle 4 Manzini, Gianmarco 4 Praetorius, Dirk 4 Ruiz-Baier, Ricardo 4 Scialò, Stefano 4 Souissi, Ali 4 Stevenson, Rob P. 4 Tavener, Simon J. 4 Zhang, Zhimin 3 Allendes, Alejandro 3 Bastian, Peter 3 Bessemoulin-Chatard, Marianne 3 Borio, Andrea 3 Chamoin, Ludovic 3 Chen, Yanping 3 Chung, Tsz Shun Eric 3 Ciarlet, Patrick jun. 3 Dakroub, Jad 3 Deuring, Paul 3 Estep, Donald J. 3 Guichard, Cindy 3 Hakula, Harri 3 Hassan, Sarah Ali 3 Hecht, Frédéric 3 Houston, Paul 3 Kern, Michel 3 Knabner, Peter 3 Kumar, Kundan 3 Mao, Shipeng 3 Martin, Vincent 3 Maryška, Jiří 3 Mghazli, Zoubida 3 Miraçi, Ani 3 Mozolevsky, Igor E. ...and 635 more Authors
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### Cited in 85 Serials

 41 Computer Methods in Applied Mechanics and Engineering 37 Journal of Computational and Applied Mathematics 35 Computers & Mathematics with Applications 35 Journal of Scientific Computing 33 Numerische Mathematik 25 SIAM Journal on Numerical Analysis 24 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 23 SIAM Journal on Scientific Computing 21 Computational Geosciences 20 Journal of Computational Physics 18 Mathematics of Computation 15 Numerical Methods for Partial Differential Equations 14 Applied Numerical Mathematics 13 Computational Methods in Applied Mathematics 12 Calcolo 10 Applied Mathematics and Computation 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 Advances in Computational Mathematics 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Numerical Algorithms 4 Mathematics and Computers in Simulation 4 Journal of Applied Mathematics and Computing 3 Computers and Fluids 3 International Journal for Numerical Methods in Fluids 3 ETNA. Electronic Transactions on Numerical Analysis 3 Journal of Numerical Mathematics 3 SIAM/ASA Journal on Uncertainty Quantification 2 Journal of Mathematical Analysis and Applications 2 BIT 2 International Journal for Numerical Methods in Engineering 2 Journal of Computational Mathematics 2 Applications of Mathematics 2 Computational Mathematics and Mathematical Physics 2 Applied Mathematical Modelling 2 Computational and Applied Mathematics 2 Nonlinear Analysis. Real World Applications 2 Foundations of Computational Mathematics 2 Acta Numerica 2 Communications in Computational Physics 2 Advances in Applied Mathematics and Mechanics 2 GEM - International Journal on Geomathematics 2 Korean Journal of Mathematics 2 Electronic Research Archive 1 Applicable Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Wave Motion 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 Numerical Functional Analysis and Optimization 1 Results in Mathematics 1 Applied Mathematics and Mechanics. (English Edition) 1 Computational Mechanics 1 Applied Mathematics Letters 1 International Journal of Computer Mathematics 1 Journal of Elasticity 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Numerical Linear Algebra with Applications 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Journal of Inverse and Ill-Posed Problems 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Analysis (München) 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 SIAM Journal on Applied Dynamical Systems 1 Central European Journal of Mathematics 1 Multiscale Modeling & Simulation 1 International Journal of Numerical Analysis and Modeling 1 Oberwolfach Reports 1 Inverse Problems in Science and Engineering 1 GAMM-Mitteilungen 1 Advances in Mathematical Physics 1 Advances in Numerical Analysis 1 Science China. Mathematics 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Afrika Matematika 1 Numerical Algebra, Control and Optimization 1 S$$\vec{\text{e}}$$MA Journal 1 ISRN Applied Mathematics 1 East Asian Journal on Applied Mathematics 1 SMAI Journal of Computational Mathematics
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### Cited in 33 Fields

 467 Numerical analysis (65-XX) 233 Partial differential equations (35-XX) 171 Fluid mechanics (76-XX) 42 Mechanics of deformable solids (74-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 19 Optics, electromagnetic theory (78-XX) 16 Geophysics (86-XX) 8 Biology and other natural sciences (92-XX) 7 Operator theory (47-XX) 7 Computer science (68-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Functional analysis (46-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 3 Approximations and expansions (41-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistics (62-XX) 3 Operations research, mathematical programming (90-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)