A PDE approach to fractional diffusion in general domains: a priori error analysis
type: Item
instance of: scholarly article
title: A PDE approach to fractional diffusion in general domains: a priori error analysis
zbMATH Open document ID: 1347.65178
author: Ricardo H. Nochetto
author: Enrique Otárola
author: Abner J. Salgado
published in: Foundations of Computational Mathematics
publication date: 2015-07-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1302.0698
review text: The article is concerned with Dirichlet boundary value problems with fractional elliptic differential operators, in particular the fractional Laplacian, on bounded \(n\)-dimensional domains. The authors propose to study an equivalent local problem on a cylindrical domain in dimension \(n +1\), in order to develop numerical discretization schemes with anisotropic tensor product finite elements. A priori error estimates for this discretization in weighted Sobolev spaces are derived. Numerical examples illustrate the method.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 6461818
zbMATH Keywords: fractional elliptic operator
zbMATH Keywords: degenerate and singular equation
zbMATH Keywords: anisotropic finite elements
reviewed by: Michael Plum
describes a project that uses: deal.ii
MaRDI profile type: Publication
OpenAlex ID: W2039427414
arXiv ID: 1302.0698
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DOI: 10.1007/S10208-014-9208-X