A fractional Laplace equation: regularity of solutions and Finite Element approximations
Numerical Analysis
2017-01-11 v3
Abstract
This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions.
Keywords
Cite
@article{arxiv.1507.08970,
title = {A fractional Laplace equation: regularity of solutions and Finite Element approximations},
author = {Gabriel Acosta and Juan Pablo Borthagaray},
journal= {arXiv preprint arXiv:1507.08970},
year = {2017}
}
Comments
Minor corrections; references added