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A Note on Multilevel Based Error Estimation

Harbrecht, Helmut and Schneider, Reinhold. (2016) A Note on Multilevel Based Error Estimation. Computational Methods in Applied Mathematics, 16 (3). pp. 447-458.

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Official URL: http://edoc.unibas.ch/43700/

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:De Gruyter
ISSN:1609-4840
e-ISSN:1609-9389
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:18 Sep 2017 10:28
Deposited On:18 Oct 2016 13:43

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