A p-version finite element method for nonlinear elliptic variational inequalities in 2D
- This article introduces and analyzes a p-version FEM for variational inequalities resulting from obstacle problems for some quasi-linear elliptic partial differential operators. We approximate the solution by controlling the obstacle condition in images of the Gauss-Lobatto points. We show existence and uniqueness for the discrete solution u p from the p-version for the obstacle problem. We prove the convergence of u p towards the solution with respect to the energy norm, and assuming some additional regularity for the solution we derive an a priori error estimate. In numerical experiments the p-version turns out to be superior to the h-version concerning the convergence rate and the number of unknowns needed to achieve a certain exactness of the approximation.
Author: | Andreas Krebs, Ernst P. Stephan |
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URL: | http://www.springerlink.com/content/p1126727200545k8/fulltext.pdf |
DOI: | https://doi.org/10.1007/s00211-006-0035-0 |
Document Type: | Article |
Language: | English |
Year of publication: | 2007 |
Tag: | FEM |
Quelle aus UBICO: | Numerische Mathematik 105(2007)3, S. 457-480, 0029-599X |
Faculty/Chair: | Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Numerische und Angewandte Mathematik |
Institution name at the time of publication: | Fakultät für Mathematik, Naturwissenschaften und Informatik (eBTU) / LS Mathematik, insbesondere Numerische und Angewandte Mathematik |