A Note on Multilevel Based Error Estimation
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 3567008
Author(s) Harbrecht, Helmut; Schneider, Reinhold
Author(s) at UniBasel Harbrecht, Helmut
Year 2016
Title A Note on Multilevel Based Error Estimation
Journal Computational Methods in Applied Mathematics
Volume 16
Number 3
Pages / Article-Number 447-458
Keywords a-posteriori error estimates, multilevel finite elements, violated Galerkin orthogonality, hierarchical error estimation
Abstract By employing the infinite multilevel representation of the residual, we derive computable bounds to estimate the distance of finite element approximations to the solution of the Poisson equation. If the finite element approximation is a Galerkin solution, the derived error estimator coincides with the standard element and edge based estimator. If Galerkin orthogonality is not satisfied, then the discrete residual additionally appears in terms of the BPX preconditioner. As a by-product of the present analysis, conditions are derived such that the hierarchical error estimation is reliable and efficient.
Publisher De Gruyter
ISSN/ISBN 1609-4840 ; 1609-9389
edoc-URL http://edoc.unibas.ch/43700/
Full Text on edoc Available
Digital Object Identifier DOI 10.1515/cmam-2016-0013
ISI-Number 000378915900005
Document type (ISI) Article

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