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Author ID: vohralik.martin Recent zbMATH articles by "Vohralík, Martin"
Published as: Vohralík, Martin; Vohralík, M.; Vohralıḱ, Martin; VohralÍk, Martin
Documents Indexed: 89 Publications since 2001
Co-Authors: 63 Co-Authors with 78 Joint Publications
1,726 Co-Co-Authors

Publications by Year

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
75
2015
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
61
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
57
2010
A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1151.65084
Vohralík, Martin
57
2007
A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Zbl 1108.65099
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
50
2006
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. Zbl 1215.65168
Jiránek, Pavel; Strakoš, Zdeněk; Vohralík, Martin
44
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
42
2011
An accurate \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
37
2007
Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. Zbl 1270.65064
Vohralík, Martin
34
2011
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Zbl 1160.65059
Vohralík, Martin
32
2008
A unified framework for a posteriori error estimation for the Stokes problem. Zbl 1301.76049
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin
32
2012
On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space \(H^1\). Zbl 1089.65124
Vohralík, Martin
30
2005
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Zbl 1201.65200
Vohralík, Martin
29
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
29
2009
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
28
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.
24
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
24
2014
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
23
2013
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Zbl 1393.76069
Vohralík, Martin; Wheeler, Mary F.
21
2013
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. Zbl 1116.65121
Vohralík, Martin
20
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
19
2014
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
19
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
18
2013
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Zbl 1453.65414
Papež, J.; Strakoš, Z.; Vohralík, M.
18
2018
\(hp\)-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
18
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
16
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
16
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
16
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
14
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
12
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
12
2015
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 1490.65282
Mallik, Gouranga; Vohralík, Martin; Yousef, Soleiman
12
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
10
2020
Mixed and nonconforming finite element methods on a system of polygons. Zbl 1112.65123
Vohralík, M.; Maryška, J.; Severýn, O.
10
2007
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
9
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
9
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
8
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
8
2017
Two types of guaranteed (and robust) a posteriori estimates for finite volume methods. Zbl 1422.65346
Vohralík, Martin
8
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
7
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
7
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
6
2018
A finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
6
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.
6
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
6
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
6
2018
Localization of the \(W^{-1,q}\) norm for local a posteriori efficiency. Zbl 07199497
Blechta, Jan; Málek, Josef; Vohralík, Martin
6
2020
A multilevel algebraic error estimator and the corresponding iterative solver with \(p\)-robust behavior. Zbl 1451.65222
Miraçi, Ani; Papež, Jan; Vohralík, Martin
6
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
5
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
5
2014
From face to element unknowns by local static condensation with application to nonconforming finite elements. Zbl 1297.65163
Vohralík, Martin; Wohlmuth, Barbara I.
5
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
5
2019
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
4
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
4
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
4
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
4
2018
Adaptive inexact semismooth Newton methods for the contact problem between two membranes. Zbl 07229481
Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
4
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
4
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
3
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
3
2020
Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems. Zbl 1470.65199
Smears, Iain; Vohralík, Martin
3
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.
3
2021
Equivalence between mixed finite element and multi-point finite volume methods. Zbl 1058.65132
Vohralík, Martin
3
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
3
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
3
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
3
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
3
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
2
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
2
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
2
2016
A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1359.76199
Vohralík, Martin
2
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
2
2021
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. Zbl 1180.65154
Vohralík, Martin
1
2005
Mixed-hybrid discrete fracture network model. Zbl 1041.76046
Vohralík, Martin; Maryška, Jiří; Severýn, Otto
1
2003
Mixed-hybrid FEM discrete fracture network model of the fracture flow. Zbl 1054.76051
Maryška, Jiří; Severý, Otto; Vohralík, Martin
1
2002
Combined nonconforming/mixed-hybrid finite element-finite volume scheme for degenerate parabolic problems. Zbl 1056.65078
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
1
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
1
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.
1
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
1
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
2
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.
3
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
2
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
2
2021
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 1490.65282
Mallik, Gouranga; Vohralík, Martin; Yousef, Soleiman
12
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
10
2020
Localization of the \(W^{-1,q}\) norm for local a posteriori efficiency. Zbl 07199497
Blechta, Jan; Málek, Josef; Vohralík, Martin
6
2020
A multilevel algebraic error estimator and the corresponding iterative solver with \(p\)-robust behavior. Zbl 1451.65222
Miraçi, Ani; Papež, Jan; Vohralík, Martin
6
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
4
2020
Adaptive inexact semismooth Newton methods for the contact problem between two membranes. Zbl 07229481
Dabaghi, Jad; Martin, Vincent; Vohralík, Martin
4
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
3
2020
Simple and robust equilibrated flux a posteriori estimates for singularly perturbed reaction-diffusion problems. Zbl 1470.65199
Smears, Iain; Vohralík, Martin
3
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
3
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
3
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
1
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
5
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
3
2019
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Zbl 1453.65414
Papež, J.; Strakoš, Z.; Vohralík, M.
18
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
6
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
6
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
6
2018
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
4
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
4
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
4
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
3
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.
1
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
16
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
16
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
8
2017
\(hp\)-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems. Zbl 1351.65082
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
18
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
2
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
75
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
12
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
4
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
24
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
19
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
9
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
5
2014
Adaptive inexact Newton methods with a posteriori stopping criteria for nonlinear diffusion PDEs. Zbl 1362.65056
Ern, Alexandre; Vohralík, Martin
61
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.
24
2013
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin
23
2013
A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows. Zbl 1393.76069
Vohralík, Martin; Wheeler, Mary F.
21
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
18
2013
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
9
2013
From face to element unknowns by local static condensation with application to nonconforming finite elements. Zbl 1297.65163
Vohralík, Martin; Wohlmuth, Barbara I.
5
2013
A unified framework for a posteriori error estimation for the Stokes problem. Zbl 1301.76049
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin
32
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
7
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
42
2011
Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. Zbl 1270.65064
Vohralík, Martin
34
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
7
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
5
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
3
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
1
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
57
2010
A posteriori error estimates including algebraic error and stopping criteria for iterative solvers. Zbl 1215.65168
Jiránek, Pavel; Strakoš, Zdeněk; Vohralík, Martin
44
2010
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Zbl 1201.65200
Vohralík, Martin
29
2010
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
28
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
16
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
29
2009
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
19
2009
A finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
6
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.
6
2009
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Zbl 1160.65059
Vohralík, Martin
32
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
14
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
8
2008
Two types of guaranteed (and robust) a posteriori estimates for finite volume methods. Zbl 1422.65346
Vohralík, Martin
8
2008
A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1151.65084
Vohralík, Martin
57
2007
An accurate \(\mathbf H\)(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
37
2007
Mixed and nonconforming finite element methods on a system of polygons. Zbl 1112.65123
Vohralík, M.; Maryška, J.; Severýn, O.
10
2007
A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1359.76199
Vohralík, Martin
2
2007
A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. Zbl 1108.65099
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
50
2006
Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. Zbl 1116.65121
Vohralík, Martin
20
2006
On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space \(H^1\). Zbl 1089.65124
Vohralík, Martin
30
2005
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. Zbl 1180.65154
Vohralík, Martin
1
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
12
2004
Equivalence between mixed finite element and multi-point finite volume methods. Zbl 1058.65132
Vohralík, Martin
3
2004
Combined nonconforming/mixed-hybrid finite element-finite volume scheme for degenerate parabolic problems. Zbl 1056.65078
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin
1
2004
Mixed-hybrid discrete fracture network model. Zbl 1041.76046
Vohralík, Martin; Maryška, Jiří; Severýn, Otto
1
2003
Mixed-hybrid FEM discrete fracture network model of the fracture flow. Zbl 1054.76051
Maryška, Jiří; Severý, Otto; Vohralík, Martin
1
2002
all top 5

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
all top 5

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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