A p-version finite element method for nonlinear elliptic variational inequalities in 2D |
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Authors: | Andreas Krebs Ernst P. Stephan |
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Affiliation: | 1. Institut für Mathematik, Brandenburgische Technische Universit?t Cottbus, 03046, Cottbus, Germany 2. Institut für Angewandte Mathematik, Universit?t Hannover, 30167, Hannover, Germany
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Abstract: | 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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Keywords: | 65N35 65K10 65N22 |
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