A Note on Multilevel Based Error Estimation-Reference-Cited by-同舟云学术

A Note on Multilevel Based Error Estimation

Published:2016-07-01 Issue:3 Volume:16 Page:447-458
ISSN:1609-9389
Container-title:Computational Methods in Applied Mathematics
language:
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Author:

Harbrecht Helmut¹,Schneider Reinhold²

Affiliation:

1. 1Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland

2. 2Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany

Abstract

AbstractBy 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.

Funder

Sino-German Science Center

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/downloadpdf/journals/cmam/16/3/article-p447.xml

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