Nonlinear discontinuous Petrov–Galerkin methods
- verfasst von
- C. Carstensen, P. Bringmann, F. Hellwig, P. Wriggers
- Abstract
The discontinuous Petrov–Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order version applies to a nonlinear uniformly convex model example and is equivalently characterized as a mixed formulation, a reduced formulation, and a weighted nonlinear least-squares method. Quasi-optimal a priori and reliable and efficient a posteriori estimates are obtained for the abstract nonlinear dPG framework for the approximation of a regular solution. The variational model example allows for a built-in guaranteed error control despite inexact solve. The subtle uniqueness of discrete minimizers is monitored in numerical examples.
- Organisationseinheit(en)
-
Institut für Kontinuumsmechanik
- Externe Organisation(en)
-
Humboldt-Universität zu Berlin (HU Berlin)
- Typ
- Artikel
- Journal
- Numerische Mathematik
- Band
- 139
- Seiten
- 529-561
- Anzahl der Seiten
- 33
- ISSN
- 0029-599X
- Publikationsdatum
- 07.2018
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Computational Mathematics, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.48550/arXiv.1710.00529 (Zugang:
Offen)
https://doi.org/10.1007/s00211-018-0947-5 (Zugang: Geschlossen)
