Convergence of adaptive FEM for elliptic obstacle problems |
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| Authors: | Michael Feischl Marcus Page Dirk Praetorius |
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| Affiliation: | Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Wien, Austria |
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| Abstract: | We treat the convergence of adaptive lowest-order FEM for some elliptic obstacle problem with affine obstacle. For error estimation, we use a residual error estimator which is an extended version of the estimator from [2] and additionally controls the data oscillations. The main result states that an appropriately weighted sum of energy error, edge residuals, and data oscillations satisfies a contraction property that leads to convergence. In addition, we discuss the generalization to the case of inhomogeneous Dirichlet data and non-affine obstacles χ ∈ H2(Ω) for which similar results are obtained. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) |
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