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
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
Bringmann, Philipp; Feischl, Michael; Miraci, Ani; Praetorius, Dirk; Streitberger, Julian On full linear convergence and optimal complexity of adaptive FEM with inexact solver. arXiv:2311.15738 Preprint, arXiv:2311.15738 [math.NA] (2023). MSC: 41A25 65N15 65N30 65N50 65Y20 BibTeX Cite \textit{P. Bringmann} et al., ``On full linear convergence and optimal complexity of adaptive FEM with inexact solver'', Preprint, arXiv:2311.15738 [math.NA] (2023) Full Text: arXiv OA License
Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan Stable implementation of adaptive IGABEM in 2D in MATLAB. (English) Zbl 1492.65039 Comput. Methods Appl. Math. 22, No. 3, 563-590 (2022). MSC: 65D07 65N38 65N50 65Y20 PDFBibTeX XMLCite \textit{G. Gantner} et al., Comput. Methods Appl. Math. 22, No. 3, 563--590 (2022; Zbl 1492.65039) Full Text: DOI arXiv
Becker, Roland; Innerberger, Michael; Praetorius, Dirk Adaptive FEM for parameter-errors in elliptic linear-quadratic parameter estimation problems. (English) Zbl 1514.65161 SIAM J. Numer. Anal. 60, No. 3, 1450-1471 (2022). Reviewer: Xiaodi Zhang (Zhengzhou) MSC: 65N30 65N50 65N15 65N12 41A25 49N10 65Y20 PDFBibTeX XMLCite \textit{R. Becker} et al., SIAM J. Numer. Anal. 60, No. 3, 1450--1471 (2022; Zbl 1514.65161) Full Text: DOI arXiv
Becker, Roland; Innerberger, Michael; Praetorius, Dirk Optimal convergence rates for goal-oriented FEM with quadratic goal functional. (English) Zbl 1476.65290 Comput. Methods Appl. Math. 21, No. 2, 267-288 (2021). MSC: 65N30 65N12 65N50 65Y20 41A25 PDFBibTeX XMLCite \textit{R. Becker} et al., Comput. Methods Appl. Math. 21, No. 2, 267--288 (2021; Zbl 1476.65290) 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
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
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
Gantner, Gregor; Praetorius, Dirk; Schimanko, Stefan Adaptive isogeometric boundary element methods with local smoothness control. (English) Zbl 07205673 Math. Models Methods Appl. Sci. 30, No. 2, 261-307 (2020). MSC: 65D07 65N38 65N50 65Y20 PDFBibTeX XMLCite \textit{G. Gantner} et al., Math. Models Methods Appl. Sci. 30, No. 2, 261--307 (2020; Zbl 07205673) Full Text: DOI arXiv
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
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. (English) Zbl 1362.65131 Numer. Math. 136, No. 1, 147-182 (2017). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N38 65D07 65N50 65Y20 PDFBibTeX XMLCite \textit{M. Feischl} et al., Numer. Math. 136, No. 1, 147--182 (2017; Zbl 1362.65131) Full Text: DOI arXiv
Feischl, Michael; Praetorius, Dirk; van der Zee, Kristoffer G. An abstract analysis of optimal goal-oriented adaptivity. (English) Zbl 1382.65392 SIAM J. Numer. Anal. 54, No. 3, 1423-1448 (2016). MSC: 65N30 65N50 65Y20 PDFBibTeX XMLCite \textit{M. Feischl} et al., SIAM J. Numer. Anal. 54, No. 3, 1423--1448 (2016; Zbl 1382.65392) Full Text: DOI arXiv
Feischl, Michael; Gantner, Gregor; Haberl, Alexander; Praetorius, Dirk; Führer, Thomas Adaptive boundary element methods for optimal convergence of point errors. (English) Zbl 1338.65259 Numer. Math. 132, No. 3, 541-567 (2016). Reviewer: Andreas Kleefeld (Jülich) MSC: 65N38 65N50 65Y20 35J05 65N12 65N15 PDFBibTeX XMLCite \textit{M. Feischl} et al., Numer. Math. 132, No. 3, 541--567 (2016; Zbl 1338.65259) Full Text: DOI
Karkulik, Michael; Pavlicek, David; Praetorius, Dirk Erratum to: “On 2D newest vertex bisection: optimality of mesh-closure and \(H^1\)-stability of \(L_2\)-projection”. (English) Zbl 1331.65167 Constr. Approx. 42, No. 3, 349-352 (2015). MSC: 65N50 65N30 65Y20 65D18 PDFBibTeX XMLCite \textit{M. Karkulik} et al., Constr. Approx. 42, No. 3, 349--352 (2015; Zbl 1331.65167) Full Text: DOI
Aurada, Markus; Ebner, Michael; Feischl, Michael; Ferraz-Leite, Samuel; Führer, Thomas; Goldenits, Petra; Karkulik, Michael; Mayr, Markus; Praetorius, Dirk HILBERT – a MATLAB implementation of adaptive 2D-BEM. \(\underline {\text H}\)ilbert \(\underline {\text I}\)s a \(\underline {\text L}\)ovely \(\underline {\text B}\)oundary \(\underline {\text E}\)lement \(\underline {\text R}\)esearch \(\underline {\text T}\)ool. (English) Zbl 1298.65183 Numer. Algorithms 67, No. 1, 1-32 (2014). MSC: 65N38 35J05 65Y15 65N15 65N50 65N12 PDFBibTeX XMLCite \textit{M. Aurada} et al., Numer. Algorithms 67, No. 1, 1--32 (2014; Zbl 1298.65183) Full Text: DOI
Karkulik, Michael; Pavlicek, David; Praetorius, Dirk On 2D newest vertex bisection: optimality of mesh-closure and \(H ^{1}\)-stability of \(L _{2}\)-projection. (English) Zbl 1302.65267 Constr. Approx. 38, No. 2, 213-234 (2013); erratum ibid. 42, No. 3, 349-352 (2015). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 65N50 65N30 65Y20 65D18 PDFBibTeX XMLCite \textit{M. Karkulik} et al., Constr. Approx. 38, No. 2, 213--234 (2013; Zbl 1302.65267) Full Text: DOI arXiv