# Wavelet boundary element methods – Adaptivity and goal-oriented error estimation

Harbrecht, Helmut and Moor, Manuela. (2018) Wavelet boundary element methods – Adaptivity and goal-oriented error estimation. Preprints Fachbereich Mathematik, 2018 (07).

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Official URL: https://edoc.unibas.ch/70171/

## Abstract

This article is dedicated to the adaptive wavelet boundary element method. It computes an approximation to the unknown solution of the boundary integral equation under consideration with a rate $N^{−s}_{dof}$, whenever the solution can be approximated with this rate in the setting determined by the underlying wavelet basis. The computational cost scale linearly in the number $N_{dof}$ of degrees of freedom. Goal-oriented error estimation for evaluating linear output functionals of the solution is also considered. An algorithm is proposed that approximately evaluates a linear output functional with a rate $N^{−(s+t)}_{dof}$, whenever the primal solution can be approximated with a rate $N^{-s}_{dof}$ and the dual solution can be approximated with a rate $N^{−t}_{dof}$, while the cost still scale linearly in $N_{dof}$. Numerical results for an acoustic scattering problem and for the point evaluation of the potential in case of the Laplace equation are reported to validate and quantify the approach.
Faculties and Departments: 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)12 Special Collections > Preprints Fachbereich Mathematik Harbrecht, Helmut Preprint Universität Basel English 10.5451/unibas-ep70171 03 Jul 2019 12:27 11 Apr 2019 20:55

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