Finite element approximation of fractional Neumann problems
Numerical Analysis
2022-12-29 v2 Numerical Analysis
Abstract
In this paper we consider approximations of Neumann problems for the integral fractional Laplacian by continuous, piecewise linear finite elements. We analyze the weak formulation of such problems, including their well-posedness and asymptotic behavior of solutions. We address the convergence of the finite element discretizations and discuss the implementation of the method. Finally, we present several numerical experiments in one- and two-dimensional domains that illustrate the method's performance as well as certain properties of solutions.
Cite
@article{arxiv.2008.06129,
title = {Finite element approximation of fractional Neumann problems},
author = {Francisco M. Bersetche and Juan Pablo Borthagaray},
journal= {arXiv preprint arXiv:2008.06129},
year = {2022}
}