Févotte, François; Rappaport, Ari; Vohralík, Martin Adaptive regularization, discretization, and linearization for nonsmooth problems based on primal-dual gap estimators. (English) Zbl 07823441 Comput. Methods Appl. Mech. Eng. 418, Part B, Article ID 116558, 33 p. (2024). MSC: 65-XX 74-XX PDFBibTeX XMLCite \textit{F. Févotte} et al., Comput. Methods Appl. Mech. Eng. 418, Part B, Article ID 116558, 33 p. (2024; Zbl 07823441) Full Text: DOI
Balci, Anna Kh.; Diening, Lars; Storn, Johannes Relaxed Kačanov scheme for the \(p\)-Laplacian with large exponent. (English) Zbl 07770185 SIAM J. Numer. Anal. 61, No. 6, 2775-2794 (2023). MSC: 35J92 65N22 65N30 PDFBibTeX XMLCite \textit{A. Kh. Balci} et al., SIAM J. Numer. Anal. 61, No. 6, 2775--2794 (2023; Zbl 07770185) Full Text: DOI arXiv
Becker, Roland; Brunner, Maximilian; Innerberger, Michael; Melenk, Jens Markus; Praetorius, Dirk Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs. (English) Zbl 1523.65090 ESAIM, Math. Model. Numer. Anal. 57, No. 4, 2193-2225 (2023). Reviewer: Bülent Karasözen (Ankara) MSC: 65N30 65N50 65N12 65N15 65Y20 41A25 35J61 PDFBibTeX XMLCite \textit{R. Becker} et al., ESAIM, Math. Model. Numer. Anal. 57, No. 4, 2193--2225 (2023; Zbl 1523.65090) Full Text: DOI arXiv
Daniel, Patrik; Vohralík, Martin Guaranteed contraction of adaptive inexact hp-refinement strategies with realistic stopping criteria. (English) Zbl 1516.65126 ESAIM, Math. Model. Numer. Anal. 57, No. 1, 329-366 (2023). Reviewer: Xiaodi Zhang (Zhengzhou) MSC: 65N30 65N15 65N12 65N50 PDFBibTeX XMLCite \textit{P. Daniel} and \textit{M. Vohralík}, ESAIM, Math. Model. Numer. Anal. 57, No. 1, 329--366 (2023; Zbl 1516.65126) Full Text: DOI
Heid, Pascal A link between the steepest descent method and fixed-point iterations. (English) Zbl 1511.90387 Optim. Lett. 17, No. 1, 27-44 (2023). MSC: 90C30 PDFBibTeX XMLCite \textit{P. Heid}, Optim. Lett. 17, No. 1, 27--44 (2023; Zbl 1511.90387) Full Text: DOI arXiv
Becker, Roland; Gantner, Gregor; Innerberger, Michael; Praetorius, Dirk Goal-oriented adaptive finite element methods with optimal computational complexity. (English) Zbl 1510.65292 Numer. Math. 153, No. 1, 111-140 (2023). MSC: 65N30 65N50 65N55 65F08 65N15 65N12 65Y20 41A25 65N22 PDFBibTeX XMLCite \textit{R. Becker} et al., Numer. Math. 153, No. 1, 111--140 (2023; Zbl 1510.65292) Full Text: DOI arXiv
Choi, Hayoung; Kim, Sang Dong; Shin, Byeong-Chun Choice of an initial guess for Newton’s method to solve nonlinear differential equations. (English) Zbl 1524.65779 Comput. Math. Appl. 117, 69-73 (2022). MSC: 65N30 76D05 65N06 65-02 65M22 76W05 35Q30 35Q31 65H10 35G10 35C05 PDFBibTeX XMLCite \textit{H. Choi} et al., Comput. Math. Appl. 117, 69--73 (2022; Zbl 1524.65779) Full Text: DOI
Heid, Pascal; Süli, Endre On the convergence rate of the Kačanov scheme for shear-thinning fluids. (English) Zbl 1483.65186 Calcolo 59, No. 1, Paper No. 4, 27 p. (2022). MSC: 65N30 65N12 35Q35 35J62 76A05 PDFBibTeX XMLCite \textit{P. Heid} and \textit{E. Süli}, Calcolo 59, No. 1, Paper No. 4, 27 p. (2022; Zbl 1483.65186) Full Text: DOI arXiv
Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P. Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. (English) Zbl 1480.35214 Comput. Methods Appl. Math. 21, No. 2, 407-422 (2021). MSC: 35J62 35J25 65N30 PDFBibTeX XMLCite \textit{P. Heid} et al., Comput. Methods Appl. Math. 21, No. 2, 407--422 (2021; Zbl 1480.35214) Full Text: DOI arXiv
Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan Rate optimality of adaptive finite element methods with respect to overall computational costs. (English) Zbl 1468.65189 Math. Comput. 90, No. 331, 2011-2040 (2021). MSC: 65N30 65N50 65Y20 65N22 65N12 65H10 65F08 65F10 41A25 PDFBibTeX XMLCite \textit{G. Gantner} et al., Math. Comput. 90, No. 331, 2011--2040 (2021; Zbl 1468.65189) Full Text: DOI arXiv
Heid, Pascal; Wihler, Thomas P. Adaptive local minimax Galerkin methods for variational problems. (English) Zbl 1481.65225 SIAM J. Sci. Comput. 43, No. 2, A1108-A1133 (2021). Reviewer: Vit Dolejsi (Praha) MSC: 65N30 65N50 35A15 35B38 35B25 35J91 47J25 49J35 49M25 58E05 58E30 65J15 PDFBibTeX XMLCite \textit{P. Heid} and \textit{T. P. Wihler}, SIAM J. Sci. Comput. 43, No. 2, A1108--A1133 (2021; Zbl 1481.65225) Full Text: DOI arXiv
Dolejší, Vít; Bartoš, Ondřej; Roskovec, Filip Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors. (English) Zbl 1524.65791 Comput. Math. Appl. 93, 178-198 (2021). MSC: 65N30 65N15 76M10 65M60 65N50 35J62 65H10 65F10 PDFBibTeX XMLCite \textit{V. Dolejší} et al., Comput. Math. Appl. 93, 178--198 (2021; Zbl 1524.65791) Full Text: DOI
Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan; Vohralík, Martin Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver. (English) Zbl 1468.65191 Numer. Math. 147, No. 3, 679-725 (2021). MSC: 65N30 65N12 65N15 65N50 35J15 68Q25 PDFBibTeX XMLCite \textit{A. Haberl} et al., Numer. Math. 147, No. 3, 679--725 (2021; Zbl 1468.65191) Full Text: DOI arXiv
Carstensen, Carsten; Nataraj, Neela Adaptive Morley FEM for the von Kármán equations with optimal convergence rates. (English) Zbl 1467.65107 SIAM J. Numer. Anal. 59, No. 2, 696-719 (2021). Reviewer: Chandrasekhar Salimath (Bengaluru) MSC: 65N30 65N12 65N15 65N50 PDFBibTeX XMLCite \textit{C. Carstensen} and \textit{N. Nataraj}, SIAM J. Numer. Anal. 59, No. 2, 696--719 (2021; Zbl 1467.65107) Full Text: DOI arXiv
Führer, Thomas; Praetorius, Dirk A short note on plain convergence of adaptive least-squares finite element methods. (English) Zbl 1451.65189 Comput. Math. Appl. 80, No. 6, 1619-1632 (2020). MSC: 65N30 65N50 65N12 65F08 65F10 PDFBibTeX XMLCite \textit{T. Führer} and \textit{D. Praetorius}, Comput. Math. Appl. 80, No. 6, 1619--1632 (2020; Zbl 1451.65189) Full Text: DOI arXiv
Heid, Pascal; Wihler, Thomas P. On the convergence of adaptive iterative linearized Galerkin methods. (English) Zbl 1448.35219 Calcolo 57, No. 3, Paper No. 24, 23 p. (2020). MSC: 35J62 65N30 PDFBibTeX XMLCite \textit{P. Heid} and \textit{T. P. Wihler}, Calcolo 57, No. 3, Paper No. 24, 23 p. (2020; Zbl 1448.35219) Full Text: DOI arXiv
Pfeiler, Carl-Martin; Praetorius, Dirk Dörfler marking with minimal cardinality is a linear complexity problem. (English) Zbl 1446.65190 Math. Comput. 89, No. 326, 2735-2752 (2020). MSC: 65N50 65N30 68Q25 PDFBibTeX XMLCite \textit{C.-M. Pfeiler} and \textit{D. Praetorius}, Math. Comput. 89, No. 326, 2735--2752 (2020; Zbl 1446.65190) Full Text: DOI arXiv
Heid, Pascal; Wihler, Thomas P. Adaptive iterative linearization Galerkin methods for nonlinear problems. (English) Zbl 07240964 Math. Comput. 89, No. 326, 2707-2734 (2020). MSC: 47H10 65N30 47J25 47H05 49M15 65J15 PDFBibTeX XMLCite \textit{P. Heid} and \textit{T. P. Wihler}, Math. Comput. 89, No. 326, 2707--2734 (2020; Zbl 07240964) Full Text: DOI arXiv
Daniel, Patrik; Ern, Alexandre; Vohralík, Martin An adaptive \(hp\)-refinement strategy with inexact solvers and computable guaranteed bound on the error reduction factor. (English) Zbl 1441.65095 Comput. Methods Appl. Mech. Eng. 359, Article ID 112607, 30 p. (2020). MSC: 65N30 65N15 65N50 PDFBibTeX XMLCite \textit{P. Daniel} et al., Comput. Methods Appl. Mech. Eng. 359, Article ID 112607, 30 p. (2020; Zbl 1441.65095) Full Text: DOI
Führer, Thomas; Haberl, Alexander; Praetorius, Dirk; Schimanko, Stefan Adaptive BEM with inexact PCG solver yields almost optimal computational costs. (English) Zbl 1412.65233 Numer. Math. 141, No. 4, 967-1008 (2019). MSC: 65N38 65N22 65F08 65N50 41A25 65Y20 45E05 65R20 PDFBibTeX XMLCite \textit{T. Führer} et al., Numer. Math. 141, No. 4, 967--1008 (2019; Zbl 1412.65233) Full Text: DOI arXiv