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## Vohralík, Martin

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 Author ID: vohralik.martin Published as: VohralÍk, Martin; Vohralík, M.; Vohralík, Martin; Vohralıḱ, Martin
 Documents Indexed: 80 Publications since 2001
all top 5

#### Co-Authors

 11 single-authored 19 Ern, Alexandre 6 Maryška, Jiří 6 Severýn, Otto 5 Cancès, Eric 5 Dusson, Geneviève 5 Maday, Yvon 5 Smears, Iain 5 Stamm, Benjamin 5 Yousef, Soleiman 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 Papež, Jan 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 Chaumont-Frelet, Théophile 1 Ciarlet, Patrick jun. 1 El Alaoui, Linda 1 Flauraud, Eric 1 Haberl, Alexander 1 Hannukainen, Antti 1 Hecht, Frédéric 1 Jiránek, Pavel 1 Málek, Josef 1 Mallik, Gouranga 1 Miraçi, Ani 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.
all top 5

#### Serials

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

#### Fields

 74 Numerical analysis (65-XX) 37 Partial differential equations (35-XX) 28 Fluid mechanics (76-XX) 5 Mechanics of deformable solids (74-XX) 3 Functional analysis (46-XX) 3 Geophysics (86-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH Open

69 Publications have been cited 953 times in 422 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
A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1151.65084
Vohralík, Martin
2007
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 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
Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. Zbl 1270.65064
Vohralík, Martin
2011
A unified framework for a posteriori error estimation for the Stokes problem. Zbl 1301.76049
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin
2012
An accurate $$\mathbf H$$(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems. Zbl 1129.65085
Ern, Alexandre; Nicaise, Serge; Vohralík, Martin
2007
Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. Zbl 1160.65059
Vohralík, Martin
2008
Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. Zbl 1201.65200
Vohralík, Martin
2010
On the discrete Poincaré-Friedrichs inequalities for nonconforming approximations of the Sobolev space $$H^1$$. Zbl 1089.65124
Vohralík, Martin
2005
A posteriori error estimation based on potential and flux reconstruction for the heat equation. Zbl 1215.65152
Ern, Alexandre; Vohralík, Martin
2010
Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems. Zbl 1190.65164
2009
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
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
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 two-phase flows. Zbl 1393.76069
Vohralík, Martin; Wheeler, Mary F.
2013
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; Vohralík, Martin
2009
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
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
$$hp$$-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
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
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
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
Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Zbl 1453.65414
Papež, J.; Strakoš, Z.; Vohralík, M.
2018
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
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
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
Four closely related equilibrated flux reconstructions for nonconforming finite elements. Zbl 1261.65117
Ern, Alexandre; Vohralík, Martin
2013
Computable a posteriori error estimates in the finite element method based on its local conservativity: improvements using local minimization. Zbl 1156.65318
2008
Mixed and nonconforming finite element methods on a system of polygons. Zbl 1112.65123
Vohralík, M.; Maryška, J.; Severýn, O.
2007
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
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
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
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 07126157
Mallik, Gouranga; Vohralík, Martin; Yousef, Soleiman
2020
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
From face to element unknowns by local static condensation with application to nonconforming finite elements. Zbl 1297.65163
Vohralík, Martin; Wohlmuth, Barbara I.
2013
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 finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
2009
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
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
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
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
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
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 perturbation-method-based a posteriori estimator for the planewave discretization of nonlinear Schrödinger equations. Zbl 1303.65077
Cancès, Éric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin
2014
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
Equivalence between mixed finite element and multi-point finite volume methods. Zbl 1058.65132
Vohralík, Martin
2004
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
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
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 finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. Zbl 1359.76199
Vohralík, Martin
2007
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 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
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
Equilibrated flux a posteriori error estimates in $$L^2(H^1)$$-norms for high-order discretizations of parabolic problems. Zbl 07323645
Ern, Alexandre; Smears, Iain; Vohralík, Martin
2019
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 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
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. Zbl 1180.65154
Vohralík, Martin
2005
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
Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. Zbl 07126157
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
Adaptive inexact semismooth Newton methods for the contact problem between two membranes. Zbl 07229481
Dabaghi, Jad; Martin, Vincent; 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 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
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
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 07323645
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
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
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
A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. Zbl 1439.74472
Vohralík, Martin; Yousef, Soleiman
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, 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
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
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. 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
A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. Zbl 1278.65138
Dolejší, Vít; 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 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
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
2009
Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. Zbl 1161.65085
Ern, Alexandre; 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 finite element discretization of the contact between two membranes. Zbl 1157.74036
Ben Belgacem, Faker; Bernardi, Christine; Blouza, Adel; Vohralík, Martin
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
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 646 Authors

 51 Vohralík, Martin 17 Ern, Alexandre 13 Radu, Florin Adrian 12 Pop, Iuliu Sorin 10 Dolejší, Vít 9 Di Pietro, Daniele Antonio 8 Saad, Mazen 7 Chen, Shaochun 7 Wheeler, Mary Fanett 7 Wihler, Thomas Pascal 7 Yousef, Soleiman 7 Zhao, Jikun 6 Ahmed, Elyes 6 Ainsworth, Mark 6 Bernardi, Christine 6 Nicaise, Serge 6 Park, Eun-Jae 6 Vejchodský, Tomáš 6 Zhang, Bei 6 Zhang, Shun 5 Achchab, Boujemaa 5 Berrone, Stefano 5 Bertrand, Fleurianne 5 Du, Shaohong 5 Georgoulis, Emmanuil H. 5 Kim, Kwang Yeon 5 Merdon, Christian 5 Nordbotten, Jan Martin 5 Papež, Jan 5 Roskovec, Filip 5 Smears, Iain 5 Starke, Gerhard 5 Verani, Marco 5 Wohlmuth, Barbara I. 5 Zhao, Lina 4 Agouzal, Abdellatif 4 Beirão da Veiga, Lourenço 4 Cai, Zhiqiang 4 Cancès, Clément 4 Cancès, Eric 4 Canuto, Claudio 4 Creusé, Emmanuel 4 Dabaghi, Jad 4 Droniou, Jérôme 4 Dusson, Geneviève 4 Erath, Christoph 4 Eymard, Robert 4 Hilhorst, Danielle 4 Japhet, Caroline 4 Langer, Ulrich 4 Maday, Yvon 4 Mu, Lin 4 Quenjel, EL Houssaine 4 Ruiz-Baier, Ricardo 4 Souissi, Ali 4 Stamm, Benjamin 4 Sun, Shuyu 4 Tavener, Simon J. 4 Wick, Thomas 4 Zhang, Zhimin 3 Allendes, Alejandro 3 Amrein, Mario 3 Bastian, Peter 3 Bessemoulin-Chatard, Marianne 3 Boffi, Daniele 3 Cangiani, Andrea 3 Carstensen, Carsten 3 Chamoin, Ludovic 3 Chen, Yanping 3 Chung, Tsz Shun Eric 3 Ciarlet, Patrick jun. 3 Deuring, Paul 3 Endtmayer, Bernhard 3 Estep, Donald J. 3 Giani, Stefano 3 Hassan, Sarah Ali 3 He, Cuiyu 3 Hecht, Frédéric 3 Kern, Michel 3 Knabner, Peter 3 Kumar, Kundan 3 Manzini, Gianmarco 3 Mao, Shipeng 3 Martin, Vincent 3 Maryška, Jiří 3 Mghazli, Zoubida 3 Mozolevsky, Igor E. 3 Mustapha, Hussein 3 Naji, Ilyas 3 Nochetto, Ricardo Horacio 3 Pieraccini, Sandra 3 Sayah, Toni 3 Scialò, Stefano 3 Šebestová, Ivana 3 Severýn, Otto 3 Stenberg, Rolf 3 Stevenson, Rob P. 3 Strakoš, Zdeněk 3 Vlasák, Miloslav 3 Xie, Xiaoping ...and 546 more Authors
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#### Cited in 73 Serials

 38 Computer Methods in Applied Mechanics and Engineering 33 Journal of Computational and Applied Mathematics 33 Journal of Scientific Computing 27 Computers & Mathematics with Applications 23 Numerische Mathematik 22 SIAM Journal on Numerical Analysis 20 Computational Geosciences 18 Journal of Computational Physics 17 SIAM Journal on Scientific Computing 16 Mathematics of Computation 16 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 15 Numerical Methods for Partial Differential Equations 11 Applied Numerical Mathematics 10 Calcolo 10 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 8 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Applied Mathematics and Computation 7 Computational Methods in Applied Mathematics 5 Advances in Computational Mathematics 4 Mathematics and Computers in Simulation 4 SIAM/ASA Journal on Uncertainty Quantification 3 Computers and Fluids 3 International Journal for Numerical Methods in Fluids 3 Numerical Algorithms 3 ETNA. Electronic Transactions on Numerical Analysis 2 Journal of Mathematical Analysis and Applications 2 International Journal for Numerical Methods in Engineering 2 Applications of Mathematics 2 Applied Mathematical Modelling 2 Nonlinear Analysis. Real World Applications 2 Foundations of Computational Mathematics 2 Journal of Numerical Mathematics 2 Journal of Applied Mathematics and Computing 2 Acta Numerica 2 GEM - International Journal on Geomathematics 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 BIT 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 Computational Mathematics and Mathematical Physics 1 International Journal of Computer Mathematics 1 Journal of Elasticity 1 Linear Algebra and its Applications 1 SIAM Journal on Mathematical Analysis 1 Numerical Linear Algebra with Applications 1 Computational and Applied Mathematics 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Journal of Inverse and Ill-Posed Problems 1 Abstract and Applied Analysis 1 SIAM Journal on Applied Dynamical Systems 1 Central European Journal of Mathematics 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 S$$\vec{\text{e}}$$MA Journal 1 ISRN Applied Mathematics 1 East Asian Journal on Applied Mathematics 1 Korean Journal of Mathematics 1 SMAI Journal of Computational Mathematics 1 Electronic Research Archive
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#### Cited in 31 Fields

 380 Numerical analysis (65-XX) 188 Partial differential equations (35-XX) 148 Fluid mechanics (76-XX) 35 Mechanics of deformable solids (74-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 14 Geophysics (86-XX) 13 Optics, electromagnetic theory (78-XX) 7 Classical thermodynamics, heat transfer (80-XX) 7 Biology and other natural sciences (92-XX) 5 Functional analysis (46-XX) 4 Ordinary differential equations (34-XX) 4 Operator theory (47-XX) 4 Computer science (68-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 General and overarching topics; collections (00-XX) 3 Probability theory and stochastic processes (60-XX) 3 Operations research, mathematical programming (90-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistics (62-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-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 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Systems theory; control (93-XX)