Frittelli, Massimo; Madzvamuse, Anotida; Sgura, Ivonne Virtual element method for elliptic bulk-surface PDEs in three space dimensions. (English) Zbl 07769115 Numer. Methods Partial Differ. Equations 39, No. 6, 4221-4247 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{M. Frittelli} et al., Numer. Methods Partial Differ. Equations 39, No. 6, 4221--4247 (2023; Zbl 07769115) Full Text: DOI arXiv OA License
Pfefferer, Johannes; Winkler, Max Finite element approximations for PDEs with irregular Dirichlet boundary data on boundary concentrated meshes. (English) Zbl 1528.35032 Comput. Methods Appl. Math. 23, No. 4, 1007-1021 (2023). MSC: 35J05 35J25 65N30 PDFBibTeX XMLCite \textit{J. Pfefferer} and \textit{M. Winkler}, Comput. Methods Appl. Math. 23, No. 4, 1007--1021 (2023; Zbl 1528.35032) Full Text: DOI
Frittelli, Massimo; Madzvamuse, Anotida; Sgura, Ivonne The bulk-surface virtual element method for reaction-diffusion PDEs: analysis and applications. (English) Zbl 07708276 Commun. Comput. Phys. 33, No. 3, 733-763 (2023). MSC: 65-XX 35K57 65M12 65M15 65M20 65M50 65M60 PDFBibTeX XMLCite \textit{M. Frittelli} et al., Commun. Comput. Phys. 33, No. 3, 733--763 (2023; Zbl 07708276) Full Text: DOI
Innerberger, Michael; Praetorius, Dirk MooAFEM: an object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs. (English) Zbl 1511.65003 Appl. Math. Comput. 442, Article ID 127731, 17 p. (2023). MSC: 65-04 65N30 65N50 68W30 PDFBibTeX XMLCite \textit{M. Innerberger} and \textit{D. Praetorius}, Appl. Math. Comput. 442, Article ID 127731, 17 p. (2023; Zbl 1511.65003) Full Text: DOI arXiv
Bulle, Raphaël; Hale, Jack S.; Lozinski, Alexei; Bordas, Stéphane P. A.; Chouly, Franz Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS project. (English) Zbl 1524.65767 Comput. Math. Appl. 131, 103-123 (2023). MSC: 65N30 65N15 35J25 65N50 35J05 65N12 74B10 PDFBibTeX XMLCite \textit{R. Bulle} et al., Comput. Math. Appl. 131, 103--123 (2023; Zbl 1524.65767) Full Text: DOI arXiv
Du, Shaohong; He, Xiaoxia Finite element approximation to optimal Dirichlet boundary control problem: a priori and a posteriori error estimates. (English) Zbl 1524.65792 Comput. Math. Appl. 131, 14-25 (2023). MSC: 65N30 49J20 49M25 65K10 65N15 35J25 PDFBibTeX XMLCite \textit{S. Du} and \textit{X. He}, Comput. Math. Appl. 131, 14--25 (2023; Zbl 1524.65792) Full Text: DOI
Liu, Yi; Chen, Wenbin; Wang, Yanqiu A weak Galerkin mixed finite element method for second order elliptic equations on 2D curved domains. (English) Zbl 1498.65204 Commun. Comput. Phys. 32, No. 4, 1094-1128 (2022). MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{Y. Liu} et al., Commun. Comput. Phys. 32, No. 4, 1094--1128 (2022; Zbl 1498.65204) Full Text: DOI arXiv
Liu, Huan; Jin, Bangti; Lu, Xiliang Imaging anisotropic conductivities from current densities. (English) Zbl 1495.35214 SIAM J. Imaging Sci. 15, No. 2, 860-891 (2022). MSC: 35R30 35R25 35J25 47J06 PDFBibTeX XMLCite \textit{H. Liu} et al., SIAM J. Imaging Sci. 15, No. 2, 860--891 (2022; Zbl 1495.35214) Full Text: DOI arXiv
Maity, Ruma Rani; Majumdar, Apala; Nataraj, Neela Error analysis of Nitsche’s and discontinuous Galerkin methods of a reduced Landau-de Gennes problem. (English) Zbl 1473.65312 Comput. Methods Appl. Math. 21, No. 1, 179-209 (2021). MSC: 65N30 35J65 65N15 PDFBibTeX XMLCite \textit{R. R. Maity} et al., Comput. Methods Appl. Math. 21, No. 1, 179--209 (2021; Zbl 1473.65312) Full Text: DOI arXiv
Du, Shaohong; Cai, Zhiqiang Adaptive finite element method for Dirichlet boundary control of elliptic partial differential equations. (English) Zbl 1480.65332 J. Sci. Comput. 89, No. 2, Paper No. 36, 25 p. (2021). MSC: 65N30 65N06 65N12 65N15 65J15 PDFBibTeX XMLCite \textit{S. Du} and \textit{Z. Cai}, J. Sci. Comput. 89, No. 2, Paper No. 36, 25 p. (2021; Zbl 1480.65332) Full Text: DOI arXiv
Kurz, Stefan; Pauly, Dirk; Praetorius, Dirk; Repin, Sergey; Sebastian, Daniel Functional a posteriori error estimates for boundary element methods. (English) Zbl 1464.65234 Numer. Math. 147, No. 4, 937-966 (2021). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 65N30 65N35 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{S. Kurz} et al., Numer. Math. 147, No. 4, 937--966 (2021; Zbl 1464.65234) Full Text: DOI arXiv
Zhang, Shun Primal-dual reduced basis methods for convex minimization variational problems: robust true solution a posteriori error certification and adaptive greedy algorithms. (English) Zbl 1456.65171 SIAM J. Sci. Comput. 42, No. 6, A3638-A3676 (2020). MSC: 65N30 65N15 65N35 65N50 65K10 PDFBibTeX XMLCite \textit{S. Zhang}, SIAM J. Sci. Comput. 42, No. 6, A3638--A3676 (2020; Zbl 1456.65171) Full Text: DOI arXiv
Winkler, Max Error estimates for variational normal derivatives and Dirichlet control problems with energy regularization. (English) Zbl 1433.49048 Numer. Math. 144, No. 2, 413-445 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 49M25 65M60 65N15 35L67 35J25 65N30 PDFBibTeX XMLCite \textit{M. Winkler}, Numer. Math. 144, No. 2, 413--445 (2020; Zbl 1433.49048) Full Text: DOI arXiv
Lederer, Philip Lukas; Merdon, Christian; Schöberl, Joachim Refined a posteriori error estimation for classical and pressure-robust Stokes finite element methods. (English) Zbl 1419.65097 Numer. Math. 142, No. 3, 713-748 (2019). MSC: 65N15 65N30 76D07 76M10 PDFBibTeX XMLCite \textit{P. L. Lederer} et al., Numer. Math. 142, No. 3, 713--748 (2019; Zbl 1419.65097) Full Text: DOI arXiv
Barbeiro, Sílvia Accuracy of a coupled mixed and Galerkin finite element approximation for poroelasticity. (English) Zbl 1422.65248 Port. Math. (N.S.) 75, No. 3-4, 249-265 (2018). MSC: 65M60 65M06 76S05 74F10 74B10 76M10 35Q35 PDFBibTeX XMLCite \textit{S. Barbeiro}, Port. Math. (N.S.) 75, No. 3--4, 249--265 (2018; Zbl 1422.65248) Full Text: DOI
Apel, Thomas; Mateos, Mariano; Pfefferer, Johannes; Rösch, Arnd Error estimates for Dirichlet control problems in polygonal domains: quasi-uniform meshes. (English) Zbl 1407.65277 Math. Control Relat. Fields 8, No. 1, 217-245 (2018). MSC: 65N30 65N15 49M05 49M25 65N12 PDFBibTeX XMLCite \textit{T. Apel} et al., Math. Control Relat. Fields 8, No. 1, 217--245 (2018; Zbl 1407.65277) Full Text: DOI arXiv
Carstensen, Carsten; Puttkammer, Sophie A low-order discontinuous Petrov-Galerkin method for the Stokes equations. (English) Zbl 1401.65131 Numer. Math. 140, No. 1, 1-34 (2018). Reviewer: Marius Ghergu (Dublin) MSC: 65N30 65N12 65N15 76D07 76M10 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{S. Puttkammer}, Numer. Math. 140, No. 1, 1--34 (2018; Zbl 1401.65131) Full Text: DOI
Lüthen, Nora; Juntunen, Mika; Stenberg, Rolf An improved a priori error analysis of Nitsche’s method for Robin boundary conditions. (English) Zbl 1448.65241 Numer. Math. 138, No. 4, 1011-1026 (2018). MSC: 65N30 65N15 35J05 PDFBibTeX XMLCite \textit{N. Lüthen} et al., Numer. Math. 138, No. 4, 1011--1026 (2018; Zbl 1448.65241) Full Text: DOI arXiv
Guignard, Diane; Nobile, Fabio; Picasso, Marco A posteriori error estimation for the steady Navier-Stokes equations in random domains. (English) Zbl 1439.76022 Comput. Methods Appl. Mech. Eng. 313, 483-511 (2017). MSC: 76D06 65N15 65N30 76M10 PDFBibTeX XMLCite \textit{D. Guignard} et al., Comput. Methods Appl. Mech. Eng. 313, 483--511 (2017; Zbl 1439.76022) Full Text: DOI
Bringmann, P.; Carstensen, C. An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. (English) Zbl 1381.76156 Numer. Math. 135, No. 2, 459-492 (2017). MSC: 76M10 65N30 65N12 65N15 65N50 76D07 65Y20 PDFBibTeX XMLCite \textit{P. Bringmann} and \textit{C. Carstensen}, Numer. Math. 135, No. 2, 459--492 (2017; Zbl 1381.76156) Full Text: DOI
Eigel, Martin; Merdon, Christian Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin finite element methods. (English) Zbl 1398.65297 SIAM/ASA J. Uncertain. Quantif. 4, 1372-1397 (2016). MSC: 65N30 35R60 47B80 60H35 65J10 65N15 PDFBibTeX XMLCite \textit{M. Eigel} and \textit{C. Merdon}, SIAM/ASA J. Uncertain. Quantif. 4, 1372--1397 (2016; Zbl 1398.65297) Full Text: DOI
Eigel, Martin; Merdon, Christian; Neumann, Johannes An adaptive multilevel Monte Carlo method with stochastic bounds for quantities of interest with uncertain data. (English) Zbl 1398.35306 SIAM/ASA J. Uncertain. Quantif. 4, 1219-1245 (2016). MSC: 35R60 35J25 47B80 60H35 65N12 65N30 65N75 PDFBibTeX XMLCite \textit{M. Eigel} et al., SIAM/ASA J. Uncertain. Quantif. 4, 1219--1245 (2016; Zbl 1398.35306) Full Text: DOI
Bringmann, P.; Carstensen, C.; Merdon, C. Guaranteed velocity error control for the pseudostress approximation of the Stokes equations. (English) Zbl 1401.76083 Numer. Methods Partial Differ. Equations 32, No. 5, 1411-1432 (2016). MSC: 76M10 65N30 65D07 65N15 PDFBibTeX XMLCite \textit{P. Bringmann} et al., Numer. Methods Partial Differ. Equations 32, No. 5, 1411--1432 (2016; Zbl 1401.76083) Full Text: DOI
Schlottbom, Matthias Error analysis of a diffuse interface method for elliptic problems with Dirichlet boundary conditions. (English) Zbl 1348.65154 Appl. Numer. Math. 109, 109-122 (2016). MSC: 65N15 35J05 65N30 65N12 PDFBibTeX XMLCite \textit{M. Schlottbom}, Appl. Numer. Math. 109, 109--122 (2016; Zbl 1348.65154) Full Text: DOI arXiv
Eigel, M.; Merdon, C. Equilibration a posteriori error estimation for convection-diffusion-reaction problems. (English) Zbl 1353.65113 J. Sci. Comput. 67, No. 2, 747-768 (2016). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65N15 65N30 65N12 35J25 35B25 PDFBibTeX XMLCite \textit{M. Eigel} and \textit{C. Merdon}, J. Sci. Comput. 67, No. 2, 747--768 (2016; Zbl 1353.65113) Full Text: DOI
Carstensen, Carsten; Eigel, Martin Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes. (English) Zbl 1336.65187 Comput. Methods Appl. Math. 16, No. 2, 213-230 (2016). MSC: 65N30 65N15 65N50 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{M. Eigel}, Comput. Methods Appl. Math. 16, No. 2, 213--230 (2016; Zbl 1336.65187) Full Text: DOI
Bermúdez, Alfredo; Gómez, Dolores; Rodríguez, Rodolfo; Venegas, Pablo Numerical analysis of a transient non-linear axisymmetric eddy current model. (English) Zbl 1443.65193 Comput. Math. Appl. 70, No. 8, 1984-2005 (2015). MSC: 65M60 78A35 PDFBibTeX XMLCite \textit{A. Bermúdez} et al., Comput. Math. Appl. 70, No. 8, 1984--2005 (2015; Zbl 1443.65193) Full Text: DOI
Carstensen, C.; Feischl, M.; Page, M.; Praetorius, D. Axioms of adaptivity. (English) Zbl 1350.65119 Comput. Math. Appl. 67, No. 6, 1195-1253 (2014). MSC: 65N30 65N38 65N15 65N50 65N12 35J25 35J60 PDFBibTeX XMLCite \textit{C. Carstensen} et al., Comput. Math. Appl. 67, No. 6, 1195--1253 (2014; Zbl 1350.65119) Full Text: DOI arXiv
Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar Adaptive stochastic Galerkin FEM. (English) Zbl 1296.65157 Comput. Methods Appl. Mech. Eng. 270, 247-269 (2014). MSC: 65N30 60H35 35J25 65N50 65N75 PDFBibTeX XMLCite \textit{M. Eigel} et al., Comput. Methods Appl. Mech. Eng. 270, 247--269 (2014; Zbl 1296.65157) Full Text: DOI Link
Feischl, M.; Page, M.; Praetorius, D. Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data. (English) Zbl 1291.65341 J. Comput. Appl. Math. 255, 481-501 (2014). MSC: 65N30 65N50 65N12 PDFBibTeX XMLCite \textit{M. Feischl} et al., J. Comput. Appl. Math. 255, 481--501 (2014; Zbl 1291.65341) Full Text: DOI arXiv
Kreuzer, Christian A note on why enforcing discrete maximum principles by a simple a posteriori cutoff is a good idea. (English) Zbl 1290.65114 Numer. Methods Partial Differ. Equations 30, No. 3, 994-1002 (2014). MSC: 65N30 35J92 35B50 PDFBibTeX XMLCite \textit{C. Kreuzer}, Numer. Methods Partial Differ. Equations 30, No. 3, 994--1002 (2014; Zbl 1290.65114) Full Text: DOI arXiv
Carstensen, C.; Merdon, C. Computational survey on a posteriori error estimators for nonconforming finite element methods for the Poisson problem. (English) Zbl 1285.65079 J. Comput. Appl. Math. 249, 74-94 (2013). MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{C. Merdon}, J. Comput. Appl. Math. 249, 74--94 (2013; Zbl 1285.65079) Full Text: DOI
Du, Qiang; Ju, Lili; Tian, Li; Zhou, Kun A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models. (English) Zbl 1327.65101 Math. Comput. 82, No. 284, 1889-1922 (2013). MSC: 65J15 65R20 65N30 65N15 PDFBibTeX XMLCite \textit{Q. Du} et al., Math. Comput. 82, No. 284, 1889--1922 (2013; Zbl 1327.65101) Full Text: DOI
Carstensen, C.; Merdon, C. A posteriori error estimator competition for conforming obstacle problems. (English) Zbl 1364.65243 Numer. Methods Partial Differ. Equations 29, No. 2, 667-692 (2013). Reviewer: Elena Resmerita (Linz) MSC: 65N30 65N15 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{C. Merdon}, Numer. Methods Partial Differ. Equations 29, No. 2, 667--692 (2013; Zbl 1364.65243) Full Text: DOI
Carstensen, C.; Merdon, C. Effective postprocessing for equilibration a posteriori error estimators. (English) Zbl 1267.65162 Numer. Math. 123, No. 3, 425-459 (2013). Reviewer: Ali Filiz (Aydin) MSC: 65N15 65N30 35J05 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{C. Merdon}, Numer. Math. 123, No. 3, 425--459 (2013; Zbl 1267.65162) Full Text: DOI
Tian, Li; Chen, Falai; Du, Qiang Adaptive finite element methods for elliptic equations over hierarchical T-meshes. (English) Zbl 1231.65222 J. Comput. Appl. Math. 236, No. 5, 878-891 (2011). MSC: 65N30 65N15 35J25 65D07 PDFBibTeX XMLCite \textit{L. Tian} et al., J. Comput. Appl. Math. 236, No. 5, 878--891 (2011; Zbl 1231.65222) Full Text: DOI
Ju, Lili; Tian, Li; Wang, Desheng A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces. (English) Zbl 1229.65192 Comput. Methods Appl. Mech. Eng. 198, No. 5-8, 716-726 (2009). MSC: 65N08 65N15 PDFBibTeX XMLCite \textit{L. Ju} et al., Comput. Methods Appl. Mech. Eng. 198, No. 5--8, 716--726 (2009; Zbl 1229.65192) Full Text: DOI Link
Yang, Ying; Zhou, Aihui A finite element recovery approach to Green’s function approximations with applications to electrostatic potential computation. (English) Zbl 1157.78002 J. Comput. Appl. Math. 225, No. 1, 202-212 (2009). MSC: 78M10 65N15 65N30 35J60 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{A. Zhou}, J. Comput. Appl. Math. 225, No. 1, 202--212 (2009; Zbl 1157.78002) Full Text: DOI
Du, Shaohong; Xie, Xiaoping Residual-based a posteriori error estimates of nonconforming finite element method for elliptic problems with Dirac delta source terms. (English) Zbl 1159.65089 Sci. China, Ser. A 51, No. 8, 1440-1460 (2008). Reviewer: Jan Lovíšek (Bratislava) MSC: 65N15 65N30 65N50 35J05 65N12 PDFBibTeX XMLCite \textit{S. Du} and \textit{X. Xie}, Sci. China, Ser. A 51, No. 8, 1440--1460 (2008; Zbl 1159.65089) Full Text: DOI
Sacchi, Roberta; Veeser, Andreas Locally efficient and reliable a posteriori error estimators for Dirichlet problems. (English) Zbl 1092.65098 Math. Models Methods Appl. Sci. 16, No. 3, 319-346 (2006). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 65N15 65N30 35J05 PDFBibTeX XMLCite \textit{R. Sacchi} and \textit{A. Veeser}, Math. Models Methods Appl. Sci. 16, No. 3, 319--346 (2006; Zbl 1092.65098) Full Text: DOI
Bartels, Sören A posteriori error analysis for time-dependent Ginzburg-Landau type equations. (English) Zbl 1073.65089 Numer. Math. 99, No. 4, 557-583 (2005). Reviewer: Kai Schneider (Marseille) MSC: 65M15 65M60 65M50 35K55 35Q72 PDFBibTeX XMLCite \textit{S. Bartels}, Numer. Math. 99, No. 4, 557--583 (2005; Zbl 1073.65089) Full Text: DOI
Bartels, S.; Carstensen, C. Averaging techniques yield reliable a posteriori finite element error control for obstacle problems. (English) Zbl 1063.65050 Numer. Math. 99, No. 2, 225-249 (2004). Reviewer: Muhammad Aslam Noor (Islamabad) MSC: 65K10 49J40 49M15 PDFBibTeX XMLCite \textit{S. Bartels} and \textit{C. Carstensen}, Numer. Math. 99, No. 2, 225--249 (2004; Zbl 1063.65050) Full Text: DOI
Bartels, Sören; Roubíček, Tomáš Linear-programming approach to nonconvex variational problems. (English) Zbl 1063.65051 Numer. Math. 99, No. 2, 251-287 (2004). Reviewer: Muhammad Aslam Noor (Islamabad) MSC: 65K10 49M37 49J20 PDFBibTeX XMLCite \textit{S. Bartels} and \textit{T. Roubíček}, Numer. Math. 99, No. 2, 251--287 (2004; Zbl 1063.65051) Full Text: DOI