Harbrecht, Helmut and Moor, Manuela.
(2019)
* Wavelet boundary element methods - Adaptivity and goal-oriented error estimation.*
In:
Advanced Finite Element Methods with Applications.
Switzerland, pp. 143-164.

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Official URL: https://edoc.unibas.ch/71203/

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## 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_{dof}^{−s}, 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_{dof}^{−(s+t)}, whenever the primal solution can be approximated with a rate N_{dof} and the dual solution can be approximated with a rate N_{dof}^{−t}, 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) |
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UniBasel Contributors: | Harbrecht, Helmut |

Item Type: | Book Section, refereed |

Book Section Subtype: | Further Contribution in a Book |

Publisher: | Springer Nature |

ISBN: | 978-3-030-14243-8 |

e-ISBN: | 978-3-030-14244-5 |

Series Name: | Lecture Notes in Computational Science and Engineering |

Issue Number: | 128 |

Note: | Publication type according to Uni Basel Research Database: Book item |

Language: | English |

Identification Number: | |

edoc DOI: | |

Last Modified: | 31 Dec 2020 02:30 |

Deposited On: | 03 Jul 2019 12:46 |

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