Error Reduction In Adaptive Finite Element Approximations Of Elliptic Obstacle Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-5088
  • 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 consistery 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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Metadaten
Author:Dietrich Braess, Carsten Carstensen, Ronald H.W. Hoppe
URN:urn:nbn:de:0296-matheon-5088
Referee:Jürgen Sprekels
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/04/28
Release Date:2008/04/16
Tag:
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N50 Mesh generation and refinement
Preprint Number:509
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