## Title data

Feist, Bernd ; Bebendorf, Mario:

**Fractional Laplacian – Quadrature Rules for Singular Double Integrals in 3D.**

*In:* Computational Methods in Applied Mathematics.
Vol. 23
(2023)
Issue 3
.
- pp. 623-645.

ISSN 1609-4840

DOI: https://doi.org/10.1515/cmam-2022-0159

## Abstract in another language

In this article, quadrature rules for the efficient computation of the stiffness matrix for the fractional Laplacian in three dimensions are presented. These rules are based on the Duffy transformation, which is a common tool for singularity removal. Here, this transformation is adapted to the needs of the fractional Laplacian in three dimensions. The integrals resulting from this Duffy transformation are regular integrals over less-dimensional domains. We present bounds on the number of Gauss points to guarantee error estimates which are of the same order of magnitude as the finite element error. The methods presented in this article can easily be adapted to other singular double integrals in three dimensions with algebraic singularities.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Keywords: | Fractional Laplacian; Non-local Operators; Quadrature Rules |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing > Chair Scientific Computing - Univ.-Prof. Dr. Mario Bebendorf |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 24 Apr 2023 09:22 |

Last Modified: | 26 Sep 2023 11:49 |

URI: | https://eref.uni-bayreuth.de/id/eprint/76083 |