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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.

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Metadaten
Author: Andreas Krebs
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
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