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.
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 |