Two-Level Error Estimation for the Integral Fractional Laplacian

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...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 23; no. 3; pp. 603 - 621
Main Authors Faustmann, Markus, Stephan, Ernst P., Wörgötter, David
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.07.2023
Walter de Gruyter GmbH
Subjects
35R11
65N30
65N50
Adaptive Methods
Algorithms
Convergence
Finite element method
Finite Element Methods
Fractional Laplacian
Grid refinement (mathematics)
Interpolation
Norms
Optimal Convergence
Two-Level Error Estimation
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Summary: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 -norms.
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2022-0195