Finite element algorithms for nonlocal minimal graphs
Juan Pablo Borthagaray, Departamento de Matemática y Estadística del Litoral, Universidad de la República, Salto, Uruguay, Wenbo Li, Ricardo H. Nochetto · Mathematics in Engineering · 2021
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.