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Efficient and Reliable Hierarchical Error Estimates for the Discretization Error of Elliptic Obstacle Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-5278
  • We present and analyze novel hierarchical a posteriori error estimates for self-adjoint elliptic obstacle problems. Our approach differs from straightforward, but non-reliable estimators~\cite{RHWHoppe_RKornhuber_1994a} by an additional extra term accounting for the deviation of the discrete free boundary in the localization step. We prove efficiency and reliability on a saturation assumption and a regularity condition on the underlying grid. Heuristic arguments suggest that the extra term is of higher order and preserves full locality. Numerical computations confirm our theoretical findings.

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Metadaten
Author:Ralf Kornhuber, Qingsong Zou
URN:urn:nbn:de:0296-matheon-5278
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/09/18
Release Date:2008/09/17
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N15 Error bounds
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Preprint Number:519
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