<div class="csl-bib-body">
<div class="csl-entry">Faustmann, M., Stephan, E. P., & Wörgötter, D. (2023). Two-level error estimation for the integral fractional Laplacian. <i>Computational Methods in Applied Mathematics</i>, <i>23</i>(3), 603–621. https://doi.org/10.1515/cmam-2022-0195</div>
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dc.identifier.issn
1609-4840
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/189950
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dc.description.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 L²-norms.
en
dc.language.iso
en
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dc.publisher
WALTER DE GRUYTER GMBH
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dc.relation.ispartof
Computational Methods in Applied Mathematics
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
Adaptive Methods
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dc.subject
Finite Element Methods
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dc.subject
Fractional Laplacian
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dc.subject
Optimal Convergence
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dc.subject
Two-Level Error Estimation
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dc.title
Two-level error estimation for the integral fractional Laplacian