On solving nonlinear variational inequalities by p-version finiteelements
- This thesis introduces and analyzes a p-version FEM for variationalinequalities resulting from obstacle problems for some nonlinearelliptic partial differential operators. We approximate the solutionby controlling the obstacle condition in images of the Gauss-Lobattopoints. We show existence and uniqueness for thediscrete solution u_p from the p-version for the obstacle problem. Weprove the convergence of u_p towards the solution with respectto the energy norm, and assuming some additional regularity for thesolution we derive an a priori error estimate. In numericalexperiments the p-version turns out to be superior to the h-versionconcerning the convergence rate and the number of unknowns needed toachieve a certain exactness of the approximation.
Author: | Andreas Krebs |
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URL: | http://edok01.tib.uni-hannover.de/edoks/e01dh04/476288029.pdf |
Document Type: | Doctoral thesis |
Language: | German |
Year of publication: | 2004 |
Tag: | Variationelle Ungleichungen; a posteriori Fehlerschätzer; großskalierte Minimierung; hp-Finite Elemente Methoden |
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 |