@article{Borthagaray2022, 
author = {Juan Pablo Borthagaray and Wenbo Li and Ricardo H. Nochetto},
title = {Finite element algorithms for nonlocal minimal graphs},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {2},
pages = {1-29},
keywords = {nonlocal minimal surfaces, finite elements, fractional diffusion},
url = {https://www.sciopen.com/article/10.3934/mine.2022016},
doi = {10.3934/mine.2022016},
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.}
}