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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 18, Issue 4

Issues

The Dual-Weighted Residual Estimator Realized on Polygonal Meshes

Steffen WeißerORCID iD: http://orcid.org/0000-0001-8507-9413 / Thomas Wick
Published Online: 2017-11-12 | DOI: https://doi.org/10.1515/cmam-2017-0046

Abstract

In this work, we realize goal-oriented error estimation using the dual-weighted residual method on general polygonal meshes. Such meshes are of current interest in various applications thanks to their great flexibility. Specifically the discrete problems are treated on BEM-based FEM. Our dual-weighted residual estimator is derived for two localization procedures. Firstly, a classical (strong) localization. Secondly, a weak form is adopted in which localization is achieved with the help of a partition-of-unity. The dual (i.e., adjoint) solution is obtained via a local higher-order approximation using a single element. Our algorithmic developments are substantiated with the help of several numerical tests.

Keywords: BEM-Based FEM; Polygonal Finite Elements; Goal-Oriented A Posteriori Error Estimation, Dual-Weighted Residual Estimator; Partition-of-Unity

MSC 2010: 65N30; 65N38; 65N50

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About the article

Received: 2017-04-25

Revised: 2017-09-01

Accepted: 2017-10-03

Published Online: 2017-11-12

Published in Print: 2018-10-01


Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 753–776, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0046.

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