The Dual-Weighted Residual Estimator Realized on Polygonal Meshes

Steffen Weißerhttp://orcid.org/0000-0001-8507-9413 1  and Thomas Wick 2
  • 1 Applied Mathematics, Saarland University, Campus, 66041, Saarbrücken, Germany
  • 2 Centre de Mathématiques Appliquées, Université Paris-Saclay, École Polytechnique, Palaiseau, France
Steffen WeißerORCID iD: http://orcid.org/0000-0001-8507-9413 and Thomas Wick
  • Centre de Mathématiques Appliquées, École Polytechnique, Université Paris-Saclay, 91128, Palaiseau, France
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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.

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