Two-Level Error Estimation for the Integral Fractional Laplacian-Reference-Cited by-同舟云学术

Two-Level Error Estimation for the Integral Fractional Laplacian

Published:2023-02-14 Issue:3 Volume:23 Page:603-621
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Faustmann Markus¹,Stephan Ernst P.²,Wörgötter David¹

Affiliation:

1. Institute of Analysis and Scientific Computing , TU Wien , Wiedner Hauptstr. 8–10, 1040 Wien , Austria

2. Institute of Applied Mathematics , Leibniz University Hannover , Welfengarten 1, 30167 Hannover , Germany

Abstract

Abstract For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott–Zhang interpolation operators in certain weighted L 2

L^{2}

-norms.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0195/pdf

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