Year: 2009
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 148–169
Abstract
We consider an adaptive finite element method (AFEM) for obstacle problems associated with linear second order elliptic boundary value problems and prove a reduction in the energy norm of the discretization error which leads to R-linear convergence. This result is shown to hold up to a consistency error due to the extension of the discrete multipliers (point functionals) to $H^{−1}$ and a possible mismatch between the continuous and discrete coincidence and noncoincidence sets. The AFEM is based on a residual-type error estimator consisting of element and edge residuals. The a posteriori error analysis reveals that the significant difference to the unconstrained case lies in the fact that these residuals only have to be taken into account within the discrete noncoincidence set. The proof of the error reduction property uses the reliability and the discrete local efficiency of the estimator as well as a perturbed Galerkin orthogonality. Numerical results are given illustrating the performance of the AFEM.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-JCM-8565
Journal of Computational Mathematics, Vol. 27 (2009), Iss. 2-3 : pp. 148–169
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Adaptive finite element methods Elliptic obstacle problems Convergence analysis.