Jayadharan, Manu; Kern, Michel; Vohralík, Martin; Yotov, Ivan A space-time multiscale mortar mixed finite element method for parabolic equations. (English) Zbl 07679124 SIAM J. Numer. Anal. 61, No. 2, 675-706 (2023). Reviewer: Shuji Yoshikawa (Oita) MSC: 65M55 65M60 65N30 65N50 65M12 65M15 65N15 65M22 65F08 65Y05 PDFBibTeX XMLCite \textit{M. Jayadharan} et al., SIAM J. Numer. Anal. 61, No. 2, 675--706 (2023; Zbl 07679124) Full Text: DOI arXiv
Ern, Alexandre; Gudi, Thirupathi; Smears, Iain; Vohralík, Martin Equivalence of local- and global-best approximations, a simple stable local commuting projector, and optimal \(hp\) approximation estimates in \(\boldsymbol{H}(\operatorname{div})\). (English) Zbl 1517.65108 IMA J. Numer. Anal. 42, No. 2, 1023-1049 (2022). MSC: 65N30 65N50 65N15 65N12 35B65 35B45 PDFBibTeX XMLCite \textit{A. Ern} et al., IMA J. Numer. Anal. 42, No. 2, 1023--1049 (2022; Zbl 1517.65108) Full Text: DOI arXiv
Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. (English) Zbl 1402.65137 Numer. Math. 140, No. 4, 1033-1079 (2018). MSC: 65N15 35P15 65N25 65N30 65N50 PDFBibTeX XMLCite \textit{E. Cancès} et al., Numer. Math. 140, No. 4, 1033--1079 (2018; Zbl 1402.65137) Full Text: DOI Link
Japhet, C.; Hassan, S. Ali; Kern, M.; Vohralík, M. Space-time domain decomposition methods and a posteriori error estimates for the heat equation. (English) Zbl 1397.65178 Dogbe, Christian (ed.), Actes du colloque “EDP-Normandie”, Caen, France, Octobre 25–26, 2017. [s.l.]: Fédération Normandie-Mathématiques (ISBN 978-2-9541221-4-4/pbk). Normandie-Mathématiques, 65-87 (2018). MSC: 65M55 PDFBibTeX XMLCite \textit{C. Japhet} et al., in: Actes du colloque ``EDP-Normandie'', Caen, France, Octobre 25--26, 2017. [s.l.]: Fédération Normandie-Mathématiques. 65--87 (2018; Zbl 1397.65178)
Hassan, Sarah Ali; Japhet, Caroline; Vohralík, Martin A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations. (English) Zbl 1397.65167 ETNA, Electron. Trans. Numer. Anal. 49, 151-181 (2018). MSC: 65M15 65M22 65M55 65F10 76S05 80A20 PDFBibTeX XMLCite \textit{S. A. Hassan} et al., ETNA, Electron. Trans. Numer. Anal. 49, 151--181 (2018; Zbl 1397.65167) Full Text: DOI Link
Ern, Alexandre; Vohralík, Martin Polynomial-degree-robust a posteriori estimates in a unified setting for conforming, nonconforming, discontinuous Galerkin, and mixed discretizations. (English) Zbl 1312.76026 SIAM J. Numer. Anal. 53, No. 2, 1058-1081 (2015). MSC: 76M10 65N15 65N30 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, SIAM J. Numer. Anal. 53, No. 2, 1058--1081 (2015; Zbl 1312.76026) Full Text: DOI
Vohralík, Martin; Wohlmuth, Barbara I. Mixed finite element methods: Implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods. (English) Zbl 1264.65198 Math. Models Methods Appl. Sci. 23, No. 5, 803-838 (2013). MSC: 65N30 35J25 65N06 65N08 PDFBibTeX XMLCite \textit{M. Vohralík} and \textit{B. I. Wohlmuth}, Math. Models Methods Appl. Sci. 23, No. 5, 803--838 (2013; Zbl 1264.65198) Full Text: DOI
Hannukainen, Antti; Stenberg, Rolf; Vohralík, Martin A unified framework for a posteriori error estimation for the Stokes problem. (English) Zbl 1301.76049 Numer. Math. 122, No. 4, 725-769 (2012). MSC: 76M10 76M12 76D07 65N15 PDFBibTeX XMLCite \textit{A. Hannukainen} et al., Numer. Math. 122, No. 4, 725--769 (2012; Zbl 1301.76049) 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
Ern, Alexandre; Vohralík, Martin Flux reconstruction and a posteriori error estimation for discontinuous Galerkin methods on general nonmatching grids. (English) Zbl 1161.65085 C. R., Math., Acad. Sci. Paris 347, No. 7-8, 441-444 (2009). MSC: 65N30 35J25 65N15 65N50 PDFBibTeX XMLCite \textit{A. Ern} and \textit{M. Vohralík}, C. R., Math., Acad. Sci. Paris 347, No. 7--8, 441--444 (2009; Zbl 1161.65085) Full Text: DOI
Vohralík, Martin A posteriori error estimates for lowest-order mixed finite element discretizations of convection-diffusion-reaction equations. (English) Zbl 1151.65084 SIAM J. Numer. Anal. 45, No. 4, 1570-1599 (2007). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65N15 65N30 35J65 PDFBibTeX XMLCite \textit{M. Vohralík}, SIAM J. Numer. Anal. 45, No. 4, 1570--1599 (2007; Zbl 1151.65084) Full Text: DOI HAL
Vohralík, Martin A posteriori error estimates for finite volume and mixed finite element discretizations of convection-diffusion-reaction equations. (English) Zbl 1359.76199 ESAIM, Proc. 18, 57-69 (2007). MSC: 76M12 76M10 65N30 65N15 PDFBibTeX XMLCite \textit{M. Vohralík}, ESAIM, Proc. 18, 57--69 (2007; Zbl 1359.76199) Full Text: DOI
Vohralík, M.; Maryška, J.; Severýn, O. Mixed and nonconforming finite element methods on a system of polygons. (English) Zbl 1112.65123 Appl. Numer. Math. 57, No. 2, 176-193 (2007). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65N30 35J25 PDFBibTeX XMLCite \textit{M. Vohralík} et al., Appl. Numer. Math. 57, No. 2, 176--193 (2007; Zbl 1112.65123) Full Text: DOI
Vohralík, Martin Equivalence between lowest-order mixed finite element and multi-point finite volume methods on simplicial meshes. (English) Zbl 1116.65121 ESAIM, Math. Model. Numer. Anal. 40, No. 2, 367-391 (2006). Reviewer: Dietrich Braess (Bochum) MSC: 65N30 35J25 65M60 35K55 PDFBibTeX XMLCite \textit{M. Vohralík}, ESAIM, Math. Model. Numer. Anal. 40, No. 2, 367--391 (2006; Zbl 1116.65121) Full Text: DOI Numdam EuDML
Eymard, Robert; Hilhorst, Danielle; Vohralík, Martin A combined finite volume-nonconforming/mixed-hybrid finite element scheme for degenerate parabolic problems. (English) Zbl 1108.65099 Numer. Math. 105, No. 1, 73-131 (2006). Reviewer: H. P. Dikshit (New Delhi) MSC: 65M60 35K57 35K65 PDFBibTeX XMLCite \textit{R. Eymard} et al., Numer. Math. 105, No. 1, 73--131 (2006; Zbl 1108.65099) Full Text: DOI
Vohralík, Martin Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties and numerical experiments. (English) Zbl 1180.65154 Handlovičová, Angela (ed.) et al., ALGORITMY 2005. 17th conference on scientific computing, Vysoké Tatry – Podbanské, Slovakia, March 13–18, 2005. Proceedings of contributed papers and posters. Bratislava: University of Technology, Faculty of Civil Engineering, Department of Mathematics and descriptive Geometry (ISBN 80-227-2192-1). 103-112 (2005). MSC: 65N30 65N08 35J25 35K57 65M60 65M08 PDFBibTeX XMLCite \textit{M. Vohralík}, in: ALGORITMY 2005. 17th conference on scientific computing, Vysoké Tatry, Podbanské, Slovakia, March 13--18, 2005. Proceedings of contributed papers and posters. Bratislava: University of Technology, Faculty of Civil Engineering, Department of Mathematics and Descriptive Geometry. 103--112 (2005; Zbl 1180.65154) Full Text: Link
Vohralík, Martin Equivalence between mixed finite element and multi-point finite volume methods. (English) Zbl 1058.65132 C. R., Math., Acad. Sci. Paris 339, No. 7, 525-528 (2004). MSC: 65N30 35J25 65N50 PDFBibTeX XMLCite \textit{M. Vohralík}, C. R., Math., Acad. Sci. Paris 339, No. 7, 525--528 (2004; Zbl 1058.65132) Full Text: DOI