A PDE approach to fractional diffusion in general domains: a priori error analysis
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.
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