arXiv:1507.08970 Abstract | arXiv Analytics

arXiv:1507.08970 [math.NA]Abstract References Reviews Resources

A fractional Laplace equation: regularity of solutions and Finite Element approximations

Published 2015-07-31Version 1

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.

Comments: 27 pages; 2 figures

Categories: math.NA

Keywords: finite element approximations, regularity, standard linear finite element method, dirichlet homogeneous fractional laplace equation

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