Chamoin, Ludovic; Legoll, Frédéric An introductory review on a posteriori error estimation in finite element computations. (English) Zbl 1528.65104 SIAM Rev. 65, No. 4, 963-1028 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N15 65B05 65N12 65N50 65-02 PDFBibTeX XMLCite \textit{L. Chamoin} and \textit{F. Legoll}, SIAM Rev. 65, No. 4, 963--1028 (2023; Zbl 1528.65104) Full Text: DOI arXiv
Li, Hanyu; Wheeler, Mary F. Dynamic local coupling for multiphase flow: a compromise between efficiency and stability. (English) Zbl 07592138 J. Comput. Phys. 469, Article ID 111535, 14 p. (2022). MSC: 65Nxx 35Jxx 35Bxx PDFBibTeX XMLCite \textit{H. Li} and \textit{M. F. Wheeler}, J. Comput. Phys. 469, Article ID 111535, 14 p. (2022; Zbl 07592138) Full Text: DOI
Leung, Wing Tat; Wang, Yating Multirate partially explicit scheme for multiscale flow problems. (English) Zbl 1492.65268 SIAM J. Sci. Comput. 44, No. 3, A1775-A1806 (2022). MSC: 65M60 65M06 65N30 65M50 76S05 76M10 76M20 35Q35 PDFBibTeX XMLCite \textit{W. T. Leung} and \textit{Y. Wang}, SIAM J. Sci. Comput. 44, No. 3, A1775--A1806 (2022; Zbl 1492.65268) Full Text: DOI arXiv
Ahusborde, Etienne; Amaziane, Brahim; Moulay, Mohamed Id High performance computing of 3D reactive multiphase flow in porous media: application to geological storage of \(\mathrm{CO_2}\). (English) Zbl 1477.86001 Comput. Geosci. 25, No. 6, 2131-2147 (2021). MSC: 86-08 65M08 65Y10 76S05 76V05 PDFBibTeX XMLCite \textit{E. Ahusborde} et al., Comput. Geosci. 25, No. 6, 2131--2147 (2021; Zbl 1477.86001) Full Text: DOI
Cancès, Clément; Droniou, Jérôme; Guichard, Cindy; Manzini, Gianmarco; Olivares, Manuela Bastidas; Pop, Iuliu Sorin Error estimates for the gradient discretisation method on degenerate parabolic equations of porous medium type. (English) Zbl 1470.76097 Di Pietro, Daniele (ed.) et al., Polyhedral methods in geosciences. Cham: Springer. SEMA SIMAI Springer Ser. 27, 37-72 (2021). MSC: 76S05 76M10 PDFBibTeX XMLCite \textit{C. Cancès} et al., SEMA SIMAI Springer Ser. 27, 37--72 (2021; Zbl 1470.76097) Full Text: DOI
Kumar, Kundan; Kyas, Svetlana; Nordbotten, Jan Martin; Repin, Sergey Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem. (English) Zbl 1524.76458 Comput. Math. Appl. 91, 122-149 (2021). MSC: 76S05 76M10 74F10 74S05 65N30 PDFBibTeX XMLCite \textit{K. Kumar} et al., Comput. Math. Appl. 91, 122--149 (2021; Zbl 1524.76458) Full Text: DOI arXiv
Ahmed, Elyes; Japhet, Caroline; Kern, Michel Space-time domain decomposition for two-phase flow between different rock types. (English) Zbl 1506.76162 Comput. Methods Appl. Mech. Eng. 371, Article ID 113294, 30 p. (2020). MSC: 76S05 74F10 74L10 PDFBibTeX XMLCite \textit{E. Ahmed} et al., Comput. Methods Appl. Mech. Eng. 371, Article ID 113294, 30 p. (2020; Zbl 1506.76162) Full Text: DOI
Papež, Jan; Rüde, Ulrich; Vohralík, Martin; Wohlmuth, Barbara Sharp algebraic and total a posteriori error bounds for \(h\) and \(p\) finite elements via a multilevel approach. Recovering mass balance in any situation. (English) Zbl 1506.76097 Comput. Methods Appl. Mech. Eng. 371, Article ID 113243, 39 p. (2020). MSC: 76M10 65N30 65N15 76S05 PDFBibTeX XMLCite \textit{J. Papež} et al., Comput. Methods Appl. Mech. Eng. 371, Article ID 113243, 39 p. (2020; Zbl 1506.76097) Full Text: DOI
Delpopolo Carciopolo, Ludovica; Formaggia, Luca; Scotti, Anna; Hajibeygi, Hadi Conservative multirate multiscale simulation of multiphase flow in heterogeneous porous media. (English) Zbl 1453.76091 J. Comput. Phys. 404, Article ID 109134, 18 p. (2020). MSC: 76M12 76S05 65M55 65M08 PDFBibTeX XMLCite \textit{L. Delpopolo Carciopolo} et al., J. Comput. Phys. 404, Article ID 109134, 18 p. (2020; Zbl 1453.76091) Full Text: DOI
Li, Hanyu; Leung, Wing Tat; Wheeler, Mary F. Sequential local mesh refinement solver with separate temporal and spatial adaptivity for non-linear two-phase flow problems. (English) Zbl 1453.76076 J. Comput. Phys. 403, Article ID 109074, 23 p. (2020). MSC: 76M10 65M60 65M50 76S05 76T06 PDFBibTeX XMLCite \textit{H. Li} et al., J. Comput. Phys. 403, Article ID 109074, 23 p. (2020; Zbl 1453.76076) Full Text: DOI arXiv
Ben Gharbia, Ibtihel; Dabaghi, Jad; Martin, Vincent; Vohralík, Martin A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints. (English) Zbl 1439.76150 Comput. Geosci. 24, No. 3, 1031-1055 (2020). MSC: 76S05 76M10 65G99 PDFBibTeX XMLCite \textit{I. Ben Gharbia} et al., Comput. Geosci. 24, No. 3, 1031--1055 (2020; Zbl 1439.76150) Full Text: DOI HAL
Ahmed, Elyes; Nordbotten, Jan Martin; Radu, Florin Adrian Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems. (English) Zbl 1524.76439 J. Comput. Appl. Math. 364, Article ID 112312, 25 p. (2020). MSC: 76S05 65N30 74F10 76M10 65F10 PDFBibTeX XMLCite \textit{E. Ahmed} et al., J. Comput. Appl. Math. 364, Article ID 112312, 25 p. (2020; Zbl 1524.76439) Full Text: DOI arXiv
Dolejší, Vít; Kuraz, Michal; Solin, Pavel Adaptive higher-order space-time discontinuous Galerkin method for the computer simulation of variably-saturated porous media flows. (English) Zbl 1481.76209 Appl. Math. Modelling 72, 276-305 (2019). MSC: 76S05 65M50 65M60 PDFBibTeX XMLCite \textit{V. Dolejší} et al., Appl. Math. Modelling 72, 276--305 (2019; Zbl 1481.76209) Full Text: DOI
Dedner, Andreas; Kane, Birane; Klöfkorn, Robert; Nolte, Martin Python framework for \(hp\)-adaptive discontinuous Galerkin methods for two-phase flow in porous media. (English) Zbl 1481.65180 Appl. Math. Modelling 67, 179-200 (2019). MSC: 65M60 76S05 76T10 PDFBibTeX XMLCite \textit{A. Dedner} et al., Appl. Math. Modelling 67, 179--200 (2019; Zbl 1481.65180) Full Text: DOI arXiv Link
Ahmed, Elyes; Ali Hassan, Sarah; Japhet, Caroline; Kern, Michel; Vohralík, Martin A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types. (English) Zbl 1432.65130 SMAI J. Comput. Math. 5, 195-227 (2019). MSC: 65M08 65M15 65M50 65M55 76S05 35K55 35K65 PDFBibTeX XMLCite \textit{E. Ahmed} et al., SMAI J. Comput. Math. 5, 195--227 (2019; Zbl 1432.65130) Full Text: DOI
Abreu, Eduardo; Bustos, Abel; Ferraz, Paola; Lambert, Wanderson A relaxation projection analytical-numerical approach in hysteretic two-phase flows in porous media. (English) Zbl 1418.76051 J. Sci. Comput. 79, No. 3, 1936-1980 (2019). MSC: 76S05 76M10 76M20 PDFBibTeX XMLCite \textit{E. Abreu} et al., J. Sci. Comput. 79, No. 3, 1936--1980 (2019; Zbl 1418.76051) Full Text: DOI
Murphy, Thomas J.; Walkington, Noel J. Control volume approximation of degenerate two-phase porous flows. (English) Zbl 1412.65190 SIAM J. Numer. Anal. 57, No. 2, 527-546 (2019). MSC: 65N12 76S05 65N08 PDFBibTeX XMLCite \textit{T. J. Murphy} and \textit{N. J. Walkington}, SIAM J. Numer. Anal. 57, No. 2, 527--546 (2019; Zbl 1412.65190) Full Text: DOI
Vohralík, Martin; Yousef, Soleiman A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows. (English) Zbl 1439.74472 Comput. Methods Appl. Mech. Eng. 331, 728-760 (2018). MSC: 74S05 76M10 65N30 65N15 74F10 76S05 PDFBibTeX XMLCite \textit{M. Vohralík} and \textit{S. Yousef}, Comput. Methods Appl. Mech. Eng. 331, 728--760 (2018; Zbl 1439.74472) Full Text: DOI HAL
Alvarez, Mario; Gatica, Gabriel N.; Ruiz-Baier, Ricardo A posteriori error estimation for an augmented mixed-primal method applied to sedimentation-consolidation systems. (English) Zbl 1415.65213 J. Comput. Phys. 367, 322-346 (2018). MSC: 65M15 76M10 65M60 76T20 PDFBibTeX XMLCite \textit{M. Alvarez} et al., J. Comput. Phys. 367, 322--346 (2018; Zbl 1415.65213) Full Text: DOI
Papež, J.; Strakoš, Z.; Vohralík, M. Estimating and localizing the algebraic and total numerical errors using flux reconstructions. (English) Zbl 1453.65414 Numer. Math. 138, No. 3, 681-721 (2018). MSC: 65N30 65N15 65N22 65F10 76M10 PDFBibTeX XMLCite \textit{J. Papež} et al., Numer. Math. 138, No. 3, 681--721 (2018; Zbl 1453.65414) Full Text: DOI Link
Kane, Birane; Klöfkorn, Robert; Gersbacher, Christoph Hp-adaptive discontinuous Galerkin methods for porous media flow. (English) Zbl 1365.76159 Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 447-456 (2017). MSC: 76M12 76M10 65M08 65M60 65M50 PDFBibTeX XMLCite \textit{B. Kane} et al., Springer Proc. Math. Stat. 200, 447--456 (2017; Zbl 1365.76159) Full Text: DOI
Baccouch, Mahboub Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation. (English) Zbl 1332.65134 Numer. Methods Partial Differ. Equations 31, No. 5, 1461-1491 (2015). Reviewer: Marius Ghergu (Dublin) MSC: 65M15 35L05 65M20 65M12 65M60 PDFBibTeX XMLCite \textit{M. Baccouch}, Numer. Methods Partial Differ. Equations 31, No. 5, 1461--1491 (2015; Zbl 1332.65134) Full Text: DOI
Di Pietro, Daniele A.; Vohralík, Martin; Yousef, Soleiman An a posteriori-based, fully adaptive algorithm with adaptive stopping criteria and mesh refinement for thermal multiphase compositional flows in porous media. (English) Zbl 1362.65097 Comput. Math. Appl. 68, No. 12, Part B, 2331-2347 (2014). MSC: 65M15 65M50 76M12 76S05 PDFBibTeX XMLCite \textit{D. A. Di Pietro} et al., Comput. Math. Appl. 68, No. 12, Part B, 2331--2347 (2014; Zbl 1362.65097) Full Text: DOI
Baccouch, Mahboub Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems. (English) Zbl 1354.65186 Appl. Math. Comput. 226, 455-483 (2014). MSC: 65M60 65M15 PDFBibTeX XMLCite \textit{M. Baccouch}, Appl. Math. Comput. 226, 455--483 (2014; Zbl 1354.65186) Full Text: DOI
Di Pietro, Daniele A.; Flauraud, Eric; Vohralík, Martin; Yousef, Soleiman A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media. (English) Zbl 1349.76323 J. Comput. Phys. 276, 163-187 (2014). MSC: 76M12 65M08 76S05 76T30 PDFBibTeX XMLCite \textit{D. A. Di Pietro} et al., J. Comput. Phys. 276, 163--187 (2014; Zbl 1349.76323) Full Text: DOI HAL
Cancès, Clément; Pop, Iuliu Sorin; Vohralík, Martin An a posteriori error estimate for vertex-centered finite volume discretizations of immiscible incompressible two-phase flow. (English) Zbl 1430.76369 Math. Comput. 83, No. 285, 153-188 (2014). MSC: 76M12 76T99 76S05 65M15 PDFBibTeX XMLCite \textit{C. Cancès} et al., Math. Comput. 83, No. 285, 153--188 (2014; Zbl 1430.76369) Full Text: DOI