Mixed-Hybrid FEM Discrete Fracture Network Model of the Fracture Flow. - Jirí Maryska; Otto Severýn; Martin Vohralík (International Conference on Computational Science (3), 2002)

Numerical methods for nonlinear elliptic and parabolic equations. Application to flow problems in porous and fractured media. (Méthodes numériques pour des équations elliptiques et paraboliques non linéaires. Application à des problèmes d'écoulement en milieux poreux et fracturés). - Martin Vohralík (2004)

A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. - Robert Eymard; Danielle Hilhorst; Martin Vohralík (Numerische Mathematik, 2006)

A Posteriori Error Estimates for Lowest-Order Mixed Finite Element Discretizations of Convection-Diffusion-Reaction Equations. - Martin Vohralík (SIAM J. Numer. Anal., 2007)

Residual flux-based a posteriori error estimates for finite volume and related locally conservative methods. - Martin Vohralík (Numerische Mathematik, 2008)

Guaranteed and robust discontinuous Galerkin a posteriori error estimates for convection-diffusion-reaction problems. - Alexandre Ern; Annette F. Stephansen; Martin Vohralík (J. Comput. Appl. Math., 2010)

Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. - Martin Vohralík (Math. Comput., 2010)

A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation. - Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2010)

A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers. - Pavel Jiránek; Zdenek Strakos; Martin Vohralík (SIAM J. Sci. Comput., 2010)

Guaranteed and Fully Robust a posteriori Error Estimates for Conforming Discretizations of Diffusion Problems with Discontinuous Coefficients. - Martin Vohralík (J. Sci. Comput., 2011)

A unified framework for a posteriori error estimation for the Stokes problem. - Antti Hannukainen; Rolf Stenberg; Martin Vohralík (Numerische Mathematik, 2012)

A Framework for Robust A Posteriori Error Control in Unsteady Nonlinear Advection-Diffusion Problems. - Vít Dolejsí; Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2013)

Robust a Posteriori Error Control and Adaptivity for Multiscale, Multinumerics, and Mortar Coupling. - Gergina Pencheva; Martin Vohralík; Mary F. Wheeler; Tim Wildey (SIAM J. Numer. Anal., 2013)

Adaptive Inexact Newton Methods with A Posteriori Stopping Criteria for Nonlinear Diffusion PDEs. - Alexandre Ern; Martin Vohralík (SIAM J. Sci. Comput., 2013)

An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. - Daniele A. Di Pietro; Martin Vohralík; Soleiman Yousef (Comput. Math. Appl., 2014)

A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. - Daniele A. Di Pietro; Eric Flauraud; Martin Vohralík; Soleiman Yousef (J. Comput. Phys., 2014)

An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. - Clément Cancès; Iuliu Sorin Pop; Martin Vohralík (Math. Comput., 2014)

Algebraic and Discretization Error Estimation by Equilibrated Fluxes for Discontinuous Galerkin Methods on Nonmatching Grids. - Vít Dolejsí; Ivana Sebestová; Martin Vohralík (J. Sci. Comput., 2015)

Adaptive regularization, linearization, and discretization and a posteriori error control for the two-phase Stefan problem. - Daniele A. Di Pietro; Martin Vohralík; Soleiman Yousef (Math. Comput., 2015)

Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations. - Alexandre Ern; Martin Vohralík (SIAM J. Numer. Anal., 2015)

A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models. - Eric Cancès; Geneviève Dusson; Yvon Maday; Benjamin Stamm; Martin Vohralík (J. Comput. Phys., 2016)

hp-Adaptation Driven by Polynomial-Degree-Robust A Posteriori Error Estimates for Elliptic Problems. - Vít Dolejsí; Alexandre Ern; Martin Vohralík (SIAM J. Sci. Comput., 2016)

Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations. - Eric Cancès; Geneviève Dusson; Yvon Maday; Benjamin Stamm; Martin Vohralík (SIAM J. Numer. Anal., 2017)

Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems. - Alexandre Ern; Iain Smears; Martin Vohralík (SIAM J. Numer. Anal., 2017)

An adaptive hp-refinement strategy with computable guaranteed bound on the error reduction factor. - Patrik Daniel; Alexandre Ern; Iain Smears; Martin Vohralík (Comput. Math. Appl., 2018)

A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations. - Sarah Ali Hassan; Caroline Japhet; Michel Kern; Martin Vohralík (Comput. Methods Appl. Math., 2018)

Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. - Eric Cancès; Geneviève Dusson; Yvon Maday; Benjamin Stamm; Martin Vohralík (Numerische Mathematik, 2018)

Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem. - Martin Cermák; Frédéric Hecht; Zuqi Tang; Martin Vohralík (Numerische Mathematik, 2018)

Estimating and localizing the algebraic and total numerical errors using flux reconstructions. - Jan Papez; Zdenek Strakos; Martin Vohralík (Numerische Mathematik, 2018)

Equivalence of local-and global-best approximations, a simple stable local commuting projector, and optimal hp approximation estimates in H(div). - Alexandre Ern; Thirupathi Gudi; Iain Smears; Martin Vohralík (CoRR, 2019)

Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (CoRR, 2020)

Stable broken H(curl) polynomial extensions and p-robust quasi-equilibrated a posteriori estimators for Maxwell's equations. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (CoRR, 2020)

Goal-oriented a posteriori error estimation for conforming and nonconforming approximations with inexact solvers. - Gouranga Mallik; Martin Vohralík; Soleiman Yousef (J. Comput. Appl. Math., 2020)

Adaptive Inexact Semismooth Newton Methods for the Contact Problem Between Two Membranes. - Jad Dabaghi; Vincent Martin; Martin Vohralík (J. Sci. Comput., 2020)

Guaranteed a posteriori bounds for eigenvalues and eigenvectors: Multiplicities and clusters. - Eric Cancès; Geneviève Dusson; Yvon Maday; Benjamin Stamm; Martin Vohralík (Math. Comput., 2020)

Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions. - Alexandre Ern; Martin Vohralík (Math. Comput., 2020)

A Multilevel Algebraic Error Estimator and the Corresponding Iterative Solver with p-Robust Behavior. - Ani Miraçi; Jan Papez; Martin Vohralík (SIAM J. Numer. Anal., 2020)

Contractive Local Adaptive Smoothing Based on Dörfler's Marking in A-Posteriori-Steered p-Robust Multigrid Solvers. - Ani Miraçi; Jan Papez; Martin Vohralík (Comput. Methods Appl. Math., 2021)

$p$-robust equilibrated flux reconstruction in ${ boldsymbol H}( mathrm{curl})$ based on local minimizations. Application to a posteriori analysis of the curl-curl problem. - Théophile Chaumont-Frelet; Martin Vohralík (CoRR, 2021)

Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations. - Clément Cancès; Flore Nabet; Martin Vohralík (Math. Comput., 2021)

On the derivation of guaranteed and p-robust a posteriori error estimates for the Helmholtz equation. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (Numerische Mathematik, 2021)

Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. - Alexander Haberl; Dirk Praetorius; Stefan Schimanko; Martin Vohralík (Numerische Mathematik, 2021)

A-Posteriori-Steered p-Robust Multigrid with Optimal Step-Sizes and Adaptive Number of Smoothing Steps. - Ani Miraçi; Jan Papez; Martin Vohralík (SIAM J. Sci. Comput., 2021)

Constrained and unconstrained stable discrete minimizations for p-robust local reconstructions in vertex patches in the de Rham complex. - Théophile Chaumont-Frelet; Martin Vohralík (CoRR, 2022)

Inexpensive polynomial-degree- and number-of-hanging-nodes-robust equilibrated flux a posteriori estimates for isogeometric analysis. - Gregor Gantner; Martin Vohralík (CoRR, 2022)

A stable local commuting projector and optimal hp approximation estimates in H(curl). - Théophile Chaumont-Frelet; Martin Vohralík (CoRR, 2022)

Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem. - Théophile Chaumont-Frelet; Alexandre Ern; Martin Vohralík (Math. Comput., 2022)

Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations. - Jan Papez; Martin Vohralík (Numer. Algorithms, 2022)

An equilibrated flux a posteriori error estimator for defeaturing problems. - Annalisa Buffa; Ondine Chanon; Denise Grappein; Rafael Vázquez Hernández; Martin Vohralík (CoRR, 2023)

Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: Adaptivity and inexact resolution. - Ibtihel Ben Gharbia; Joëlle Ferzly; Martin Vohralík; Soleiman Yousef (J. Comput. Appl. Math., 2023)

Adaptive inexact smoothing Newton method for a nonconforming discretization of a variational inequality. - Ibtihel Ben Gharbia; Joëlle Ferzly; Martin Vohralík; Soleiman Yousef (Comput. Math. Appl., 2023)

A Space-Time Multiscale Mortar Mixed Finite Element Method for Parabolic Equations. - Manu Jayadharan; Michel Kern; Martin Vohralík; Ivan Yotov (SIAM J. Numer. Anal., 2023)

(p ) -Robust Equilibrated Flux Reconstruction in ( boldsymbol{H}( textrm{curl}) ) Based on Local Minimizations: Application to a Posteriori Analysis of the Curl-Curl Problem. - Théophile Chaumont-Frelet; Martin Vohralík (SIAM J. Numer. Anal., 2023)

A posteriori error estimates for the Richards equation. - K. Mitra; Martin Vohralík (Math. Comput., 2023)

A-posteriori-steered p-robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems. - Ani Miraçi; Jan Papez; Martin Vohralík; Ivan Yotov (CoRR, 2024)

Discrete Poincaré inequalities: a review on proofs, equivalent formulations, and behavior of constants. - Alexandre Ern; Johnny Guzmán; Pratyush Potu; Martin Vohralík (CoRR, 2024)

An Equilibrated Flux A Posteriori Error Estimator for Defeaturing Problems. - Annalisa Buffa; Ondine Chanon; Denise Grappein; Rafael Vázquez; Martin Vohralík (SIAM J. Numer. Anal., 2024)

A stable local commuting projector and optimal hp approximation estimates in $ varvec{H}( textrm{curl})$. - Théophile Chaumont-Frelet; Martin Vohralík (Numerische Mathematik, 2024)

Local L2-bounded commuting projections using discrete local problems on Alfeld splits. - Alexandre Ern; Johnny Guzmán; Pratyush Potu; Martin Vohralík (CoRR, 2025)

A posteriori error estimates and adaptivity for locally conservative methods. Inexpensive implementation and evaluation, polytopal meshes, iterative linearization and algebraic solvers, and applications to complex porous media flows. - Martin Vohralík; Soleiman Yousef (CoRR, 2025)

A quasi-interpolation operator yielding fully computable error bounds. - Théophile Chaumont-Frelet; Martin Vohralík (CoRR, 2025)