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Erschienen in: Foundations of Computational Mathematics 3/2015

01.06.2015

A PDE Approach to Fractional Diffusion in General Domains: A Priori Error Analysis

verfasst von: Ricardo H. Nochetto, Enrique Otárola, Abner J. Salgado

Erschienen in: Foundations of Computational Mathematics | Ausgabe 3/2015

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Abstract

The purpose of this work is to study solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the Dirichlet-to-Neumann map for a degenerate/singular elliptic problem posed on a semi-infinite cylinder, which we analyze in the framework of weighted Sobolev spaces. Motivated by the rapid decay of the solution to this problem, we propose a truncation that is suitable for numerical approximation. We discretize this truncation using first degree tensor product finite elements. We derive a priori error estimates in weighted Sobolev spaces. The estimates exhibit optimal regularity but suboptimal order for quasi-uniform meshes. For anisotropic meshes instead, they are quasi-optimal in both order and regularity. We present numerical experiments to illustrate the method’s performance.

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Metadaten
Titel
A PDE Approach to Fractional Diffusion in General Domains: A Priori Error Analysis
verfasst von
Ricardo H. Nochetto
Enrique Otárola
Abner J. Salgado
Publikationsdatum
01.06.2015
Verlag
Springer US
Erschienen in
Foundations of Computational Mathematics / Ausgabe 3/2015
Print ISSN: 1615-3375
Elektronische ISSN: 1615-3383
DOI
https://doi.org/10.1007/s10208-014-9208-x

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