Papež, Jan; Vohralík, Martin Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations. (English) Zbl 1492.65328 Numer. Algorithms 89, No. 1, 371-407 (2022). MSC: 65N30 65N22 65N50 65N15 76M10 65F10 PDFBibTeX XMLCite \textit{J. Papež} and \textit{M. Vohralík}, Numer. Algorithms 89, No. 1, 371--407 (2022; Zbl 1492.65328) Full Text: DOI HAL
Ern, Alexandre; Smears, Iain; Vohralík, Martin Equilibrated flux a posteriori error estimates in \(L^2(H^1)\)-norms for high-order discretizations of parabolic problems. (English) Zbl 1467.65092 IMA J. Numer. Anal. 39, No. 3, 1158-1179 (2019). Reviewer: Jan Giesselmann (Darmstadt) MSC: 65M60 65N30 65M15 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 39, No. 3, 1158--1179 (2019; Zbl 1467.65092) Full Text: DOI arXiv
Dolejší, Vít; Ern, Alexandre; Vohralík, Martin A framework for robust a posteriori error control in unsteady nonlinear advection-diffusion problems. (English) Zbl 1278.65138 SIAM J. Numer. Anal. 51, No. 2, 773-793 (2013). Reviewer: Gisbert Stoyan (Budapest) MSC: 65M15 65M50 35K65 65M06 65M60 PDFBibTeX XMLCite \textit{V. Dolejší} et al., SIAM J. Numer. Anal. 51, No. 2, 773--793 (2013; Zbl 1278.65138) Full Text: DOI HAL
Pencheva, Gergina V.; Vohralík, Martin; Wheeler, Mary F.; Wildey, Tim Robust a posteriori error control and adaptivity for multiscale, multinumerics, and mortar coupling. (English) Zbl 1267.65165 SIAM J. Numer. Anal. 51, No. 1, 526-554 (2013). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N15 65N30 35J25 65N55 65N50 PDFBibTeX XMLCite \textit{G. V. Pencheva} et al., SIAM J. Numer. Anal. 51, No. 1, 526--554 (2013; Zbl 1267.65165) Full Text: DOI HAL
Vohralík, Martin Guaranteed and fully robust a posteriori error estimates for conforming discretizations of diffusion problems with discontinuous coefficients. (English) Zbl 1270.65064 J. Sci. Comput. 46, No. 3, 397-438 (2011). MSC: 65N15 65N30 65N08 76M10 76M12 76R50 PDFBibTeX XMLCite \textit{M. Vohralík}, J. Sci. Comput. 46, No. 3, 397--438 (2011; Zbl 1270.65064) Full Text: DOI HAL
Ern, Alexandre; Vohralıḱ, Martin A unified framework for a posteriori error estimation in elliptic and parabolic problems with application to finite volumes. (English) Zbl 1246.65162 Fořt, Jaroslav (ed.) et al., Finite volumes for complex applications VI: Problems and perspectives. FVCA 6, international symposium, Prague, Czech Republich, June 6–10, 2011. Vol. 1 and 2. Berlin: Springer (ISBN 978-3-642-20670-2/hbk; 978-3-642-20671-9/ebook). Springer Proceedings in Mathematics 4, 821-837 (2011). MSC: 65M08 65M15 65M50 65N08 65N15 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralıḱ}, Springer Proc. Math. 4, 821--837 (2011; Zbl 1246.65162) Full Text: DOI
El Alaoui, Linda; Ern, Alexandre; Vohralík, Martin Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems. (English) Zbl 1230.65118 Comput. Methods Appl. Mech. Eng. 200, No. 37-40, 2782-2795 (2011). MSC: 65N15 65N22 PDFBibTeX XMLCite \textit{L. El Alaoui} et al., Comput. Methods Appl. Mech. Eng. 200, No. 37--40, 2782--2795 (2011; Zbl 1230.65118) Full Text: DOI HAL
Hilhorst, Danielle; Vohralík, Martin A posteriori error estimates for combined finite volume-finite element discretizations of reactive transport equations on nonmatching grids. (English) Zbl 1225.76212 Comput. Methods Appl. Mech. Eng. 200, No. 5-8, 597-613 (2011). MSC: 76M12 76M10 76V05 76R10 65M15 PDFBibTeX XMLCite \textit{D. Hilhorst} and \textit{M. Vohralík}, Comput. Methods Appl. Mech. Eng. 200, No. 5--8, 597--613 (2011; Zbl 1225.76212) Full Text: DOI
Vohralík, Martin Unified primal formulation-based a priori and a posteriori error analysis of mixed finite element methods. (English) Zbl 1201.65200 Math. Comput. 79, No. 272, 2001-2032 (2010). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65N15 65N30 35J25 PDFBibTeX XMLCite \textit{M. Vohralík}, Math. Comput. 79, No. 272, 2001--2032 (2010; Zbl 1201.65200) Full Text: DOI