Research article

Finite element algorithms for nonlocal minimal graphs

  • Received: 26 May 2021 Accepted: 07 July 2021 Published: 20 July 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.

    Citation: Juan Pablo Borthagaray, Wenbo Li, Ricardo H. Nochetto. Finite element algorithms for nonlocal minimal graphs[J]. Mathematics in Engineering, 2022, 4(2): 1-29. doi: 10.3934/mine.2022016

    Related Papers:

  • 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.



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