Open AccessFinite element algorithms for nonlocal minimal graphs
Author(s) -
Juan Pablo Borthagaray,
Wenbo Li,
Ricardo H. Nochetto
Publication year - 2021
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2022016
Subject(s) - mathematics , piecewise linear function , discretization , bounded function , truncation (statistics) , finite element method , bounded variation , parametric statistics , curvature , algorithm , discrete mathematics , mathematical analysis , geometry , thermodynamics , statistics , physics
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.