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A note on multilevel based error estimation

Harbrecht, Helmut and Schneider, Reinhold. (2016) A note on multilevel based error estimation. Preprints Fachbereich Mathematik, 2016 (03).

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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 the reliable and efficient.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:22 Apr 2019 14:59
Deposited On:28 Mar 2019 09:51

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