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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.

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Metadaten
Author: Andreas Krebs, Ernst P. Stephan
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
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