Finite element algorithms for nonlocal minimal graphs
Numerical Analysis
2021-05-14 v1 Numerical Analysis
Abstract
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.
Cite
@article{arxiv.2105.06079,
title = {Finite element algorithms for nonlocal minimal graphs},
author = {Juan Pablo Borthagaray and Wenbo Li and Ricardo H. Nochetto},
journal= {arXiv preprint arXiv:2105.06079},
year = {2021}
}