Gaspoz, Fernando D.; Siebert, Kunibert; Kreuzer, Christian; Ziegler, Daniel A. A convergent time-space adaptive dG\((s)\) finite element method for parabolic problems motivated by equal error distribution. (English) Zbl 1461.65239 IMA J. Numer. Anal. 39, No. 2, 650-686 (2019). MSC: 65M60 65M50 65M12 35K90 PDFBibTeX XMLCite \textit{F. D. Gaspoz} et al., IMA J. Numer. Anal. 39, No. 2, 650--686 (2019; Zbl 1461.65239) Full Text: DOI arXiv
Rösch, A.; Siebert, K. G.; Steinig, Simeon Reliable a posteriori error estimation for state-constrained optimal control. (English) Zbl 1380.49003 Comput. Optim. Appl. 68, No. 1, 121-162 (2017). Reviewer: Hussain A. El-Saify (Beni Suef) MSC: 49J20 49M25 80M10 65M15 35J99 PDFBibTeX XMLCite \textit{A. Rösch} et al., Comput. Optim. Appl. 68, No. 1, 121--162 (2017; Zbl 1380.49003) Full Text: DOI
Kreuzer, Christian; Möller, Christian A.; Schmidt, Alfred; Siebert, Kunibert G. Design and convergence analysis for an adaptive discretization of the heat equation. (English) Zbl 1261.65092 IMA J. Numer. Anal. 32, No. 4, 1375-1403 (2012). Reviewer: Yaşar Sözen (Istanbul) MSC: 65M12 65M06 65M60 35K05 65M15 PDFBibTeX XMLCite \textit{C. Kreuzer} et al., IMA J. Numer. Anal. 32, No. 4, 1375--1403 (2012; Zbl 1261.65092) Full Text: DOI
Siebert, Kunibert G. Mathematically founded design of adaptive finite element software. (English) Zbl 1250.65142 Naldi, Giovanni (ed.) et al., Multiscale and adaptivity: Modeling, numerics and applications. C.I.M.E. summer school, Cetraro, Italy, July 6–11, 2009. Berlin: Springer; Firenze: Fondazione CIME Roberto Conti (ISBN 978-3-642-24078-2/pbk; 978-3-642-24079-9/ebook). Lecture Notes in Mathematics 2040, 227-309 (2012). MSC: 65N30 65N15 65N50 35J05 35J25 65Y15 PDFBibTeX XMLCite \textit{K. G. Siebert}, Lect. Notes Math. 2040, 227--309 (2012; Zbl 1250.65142) Full Text: DOI
Siebert, Kunibert G. A convergence proof for adaptive finite elements without lower bound. (English) Zbl 1225.65101 IMA J. Numer. Anal. 31, No. 3, 947-970 (2011). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N12 65N30 35J25 35J40 PDFBibTeX XMLCite \textit{K. G. Siebert}, IMA J. Numer. Anal. 31, No. 3, 947--970 (2011; Zbl 1225.65101) Full Text: DOI
Kreuzer, Christian; Siebert, Kunibert G. Decay rates of adaptive finite elements with Dörfler marking. (English) Zbl 1219.65133 Numer. Math. 117, No. 4, 679-716 (2011). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N12 65N50 65N15 35J25 PDFBibTeX XMLCite \textit{C. Kreuzer} and \textit{K. G. Siebert}, Numer. Math. 117, No. 4, 679--716 (2011; Zbl 1219.65133) Full Text: DOI
Nochetto, Ricardo H.; Siebert, Kunibert G.; Veeser, Andreas Theory of adaptive finite element methods: An introduction. (English) Zbl 1190.65176 DeVore, Ronald (ed.) et al., Multiscale, nonlinear and adaptive approximation. Dedicated to Wolfgang Dahmen on the occasion of his 60th birthday. Berlin: Springer (ISBN 978-3-642-03412-1/hbk; 978-3-642-03413-8/ebook). 409-542 (2009). MSC: 65N30 65-02 35J25 65N12 65N50 PDFBibTeX XMLCite \textit{R. H. Nochetto} et al., in: Multiscale, nonlinear and adaptive approximation. Dedicated to Wolfgang Dahmen on the occasion of his 60th birthday. Berlin: Springer. 409--542 (2009; Zbl 1190.65176) Full Text: DOI
Cascon, J. Manuel; Kreuzer, Christian; Nochetto, Ricardo H.; Siebert, Kunibert G. Quasi-optimal convergence rate for an adaptive finite element method. (English) Zbl 1176.65122 SIAM J. Numer. Anal. 46, No. 5, 2524-2550 (2008). MSC: 65N12 65N15 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{J. M. Cascon} et al., SIAM J. Numer. Anal. 46, No. 5, 2524--2550 (2008; Zbl 1176.65122) Full Text: DOI
Cascon, J. Manuel; Nochetto, Ricardo H.; Siebert, Kunibert G. Design and convergence of AFEM in \(H\)(div). (English) Zbl 1144.65064 Math. Models Methods Appl. Sci. 17, No. 11, 1849-1881 (2007). Reviewer: Constantin Popa (Constanţa) MSC: 65N12 65N15 65N30 35J25 65N50 35R05 PDFBibTeX XMLCite \textit{J. M. Cascon} et al., Math. Models Methods Appl. Sci. 17, No. 11, 1849--1881 (2007; Zbl 1144.65064) Full Text: DOI
Nochetto, Ricardo H.; Schmidt, Alfred; Siebert, Kunibert G.; Veeser, Andreas Pointwise a posteriori error estimates for monotone semi-linear equations. (English) Zbl 1104.65107 Numer. Math. 104, No. 4, 515-538 (2006). Reviewer: Dietrich Braess (Bochum) MSC: 65N15 65N30 35J85 35J65 PDFBibTeX XMLCite \textit{R. H. Nochetto} et al., Numer. Math. 104, No. 4, 515--538 (2006; Zbl 1104.65107) Full Text: DOI
Nochetto, Ricardo H.; Siebert, Kunibert G.; Veeser, Andreas Fully localized a posteriori error estimators and barrier sets for contact problems. (English) Zbl 1095.65099 SIAM J. Numer. Anal. 42, No. 5, 2118-2135 (2005). Reviewer: Michel Bernadou (Paris La Defense) MSC: 65N15 65N30 35J85 65K10 49J40 35R35 PDFBibTeX XMLCite \textit{R. H. Nochetto} et al., SIAM J. Numer. Anal. 42, No. 5, 2118--2135 (2005; Zbl 1095.65099) Full Text: DOI
Schmidt, Alfred; Siebert, Kunibert G. Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM. (English) Zbl 1068.65138 Lecture Notes in Computational Science and Engineering 42. Berlin: Springer (ISBN 3-540-22842-X/hbk). xii, 315 p. (2005). Reviewer: Christian Grossmann (Dresden) MSC: 65N30 65N50 65-02 65Y15 65M60 65M50 35J05 35K05 35K57 PDFBibTeX XMLCite \textit{A. Schmidt} and \textit{K. G. Siebert}, Design of adaptive finite element software. The finite element toolbox ALBERTA. With CD-ROM. Berlin: Springer (2005; Zbl 1068.65138)
Dziuk, Gerhard; Boschert, Stefan; Schmidt, Alfred; Siebert, Kunibert G.; Bänsch, Eberhard; Benz, Klaus-Werner; Kaiser, Thomas Simulation of industrial crystal growth by the vertical Bridgman method. (English) Zbl 1052.80507 Jäger, Willi (ed.) et al., Mathematics – key technology for the future. Joint projects between universities and industry. Berlin: Springer (ISBN 3-540-44220-0/hbk). 315-342 (2003). MSC: 80A99 82D25 74N05 80A22 35R35 00A72 PDFBibTeX XMLCite \textit{G. Dziuk} et al., in: Mathematics -- key technology for the future. Joint projects between universities and industry. Berlin: Springer. 315--342 (2003; Zbl 1052.80507)
Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. Local problems on stars: A posteriori error estimators, convergence, and performance. (English) Zbl 1019.65083 Math. Comput. 72, No. 243, 1067-1097 (2003). Reviewer: Ll.G.Chambers (Bangor) MSC: 65N15 65N12 65N30 65N50 35J05 65Y20 PDFBibTeX XMLCite \textit{P. Morin} et al., Math. Comput. 72, No. 243, 1067--1097 (2003; Zbl 1019.65083) Full Text: DOI
Morin, Pedro; Nochetto, Ricardo H.; Siebert, Kunibert G. Convergence of adaptive finite element methods. (English) Zbl 1016.65074 SIAM Rev. 44, No. 4, 631-658 (2002). Reviewer: Ll.G.Chambers (Bangor) MSC: 65N12 65N50 35Q30 65Y20 65N15 35J25 65N30 PDFBibTeX XMLCite \textit{P. Morin} et al., SIAM Rev. 44, No. 4, 631--658 (2002; Zbl 1016.65074) Full Text: DOI
Schmidt, A.; Siebert, K. G. Abstract data structures for a finite element package: Design principles of ALBERT. (English) Zbl 0944.65529 ZAMM, Z. Angew. Math. Mech. 79, Suppl. 1, S49-S52 (1999). MSC: 65N30 35J25 65Y15 65N50 65N15 PDFBibTeX XMLCite \textit{A. Schmidt} and \textit{K. G. Siebert}, ZAMM, Z. Angew. Math. Mech. 79, S49--S52 (1999; Zbl 0944.65529) Full Text: DOI
Siebert, Kunibert G. An a posteriori error estimator for anisotropic refinement. (English) Zbl 0873.65098 Numer. Math. 73, No. 3, 373-398 (1996). Reviewer: R.R.D.Lazarov (College Station) MSC: 65N15 65N30 65N50 35J25 PDFBibTeX XMLCite \textit{K. G. Siebert}, Numer. Math. 73, No. 3, 373--398 (1996; Zbl 0873.65098) Full Text: DOI