Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr Finite element methods respecting the discrete maximum principle for convection-diffusion equations. (English) Zbl 07805455 SIAM Rev. 66, No. 1, 3-88 (2024). MSC: 65M60 65M06 65N30 65N50 76R50 35B35 35J05 35B50 35B09 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., SIAM Rev. 66, No. 1, 3--88 (2024; Zbl 07805455) Full Text: DOI arXiv
Barrenechea, Gabriel R.; Poza, Abner H.; Yorston, Heather A stabilised finite element method for the convection-diffusion-reaction equation in mixed form. (English) Zbl 1440.65178 Comput. Methods Appl. Mech. Eng. 339, 389-415 (2018). MSC: 65N30 35K20 35K57 65N12 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., Comput. Methods Appl. Mech. Eng. 339, 389--415 (2018; Zbl 1440.65178) Full Text: DOI
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, Richard A unified analysis of algebraic flux correction schemes for convection-diffusion equations. (English) Zbl 1422.65368 S\(\vec{\text{e}}\)MA J. 75, No. 4, 655-685 (2018). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., S\(\vec{\text{e}}\)MA J. 75, No. 4, 655--685 (2018; Zbl 1422.65368) Full Text: DOI
Barrenechea, Gabriel R.; Burman, Erik; Karakatsani, Fotini Blending low-order stabilised finite element methods: a positivity-preserving local projection method for the convection-diffusion equation. (English) Zbl 1439.65144 Comput. Methods Appl. Mech. Eng. 317, 1169-1193 (2017). MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., Comput. Methods Appl. Mech. Eng. 317, 1169--1193 (2017; Zbl 1439.65144) Full Text: DOI
Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard Fully computable error estimation of a nonlinear, positivity-preserving discretization of the convection-diffusion-reaction equation. (English) Zbl 1373.65065 SIAM J. Sci. Comput. 39, No. 5, A1903-A1927 (2017). MSC: 65M15 35K57 65M60 65M50 PDFBibTeX XMLCite \textit{A. Allendes} et al., SIAM J. Sci. Comput. 39, No. 5, A1903--A1927 (2017; Zbl 1373.65065) Full Text: DOI
Barrenechea, Gabriel R.; Knobloch, Petr Analysis of a group finite element formulation. (English) Zbl 1367.65141 Appl. Numer. Math. 118, 238-248 (2017). MSC: 65M60 35K57 65M12 65M15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} and \textit{P. Knobloch}, Appl. Numer. Math. 118, 238--248 (2017; Zbl 1367.65141) Full Text: DOI Link
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes. (English) Zbl 1360.65275 Math. Models Methods Appl. Sci. 27, No. 3, 525-548 (2017). MSC: 65N30 65N12 65N15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., Math. Models Methods Appl. Sci. 27, No. 3, 525--548 (2017; Zbl 1360.65275) Full Text: DOI
Barrenechea, Gabriel R.; Burman, Erik; Karakatsani, Fotini Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes. (English) Zbl 1395.65137 Numer. Math. 135, No. 2, 521-545 (2017). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65N30 65N12 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., Numer. Math. 135, No. 2, 521--545 (2017; Zbl 1395.65137) Full Text: DOI arXiv
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr Analysis of algebraic flux correction schemes. (English) Zbl 1346.65048 SIAM J. Numer. Anal. 54, No. 4, 2427-2451 (2016). MSC: 65M60 65M12 35K57 35K90 35B50 65M15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., SIAM J. Numer. Anal. 54, No. 4, 2427--2451 (2016; Zbl 1346.65048) Full Text: DOI
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr Some analytical results for an algebraic flux correction scheme for a steady convection-diffusion equation in one dimension. (English) Zbl 1332.65105 IMA J. Numer. Anal. 35, No. 4, 1729-1756 (2015). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 65L10 65L60 34B15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., IMA J. Numer. Anal. 35, No. 4, 1729--1756 (2015; Zbl 1332.65105) Full Text: DOI
Ainsworth, Mark; Allendes, Alejandro; Barrenechea, Gabriel R.; Rankin, Richard Fully computable a posteriori error bounds for stabilised FEM approximations of convection-reaction-diffusion problems in three dimensions. (English) Zbl 1455.65207 Int. J. Numer. Methods Fluids 73, No. 9, 765-790 (2013). MSC: 65N30 65N15 76M10 PDFBibTeX XMLCite \textit{M. Ainsworth} et al., Int. J. Numer. Methods Fluids 73, No. 9, 765--790 (2013; Zbl 1455.65207) Full Text: DOI Link
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. (English) Zbl 1303.65082 ESAIM, Math. Model. Numer. Anal. 47, No. 5, 1335-1366 (2013). Reviewer: Angela Handlovičová (Bratislava) MSC: 65M60 35K57 65M12 65M15 PDFBibTeX XMLCite \textit{G. R. Barrenechea} et al., ESAIM, Math. Model. Numer. Anal. 47, No. 5, 1335--1366 (2013; Zbl 1303.65082) Full Text: DOI