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.

翻译：我们讨论分层高原的计算和定性方面,以及受外部数据为子图的外缘界域规定的分数平均曲线问题。我们从能源最小化的角度重现这些问题,用分片线性有限元素将后者分解。在计算离散解决方案时,我们提出并研究梯度流和牛顿方案,并量化Drichlet数据截断的影响。我们还提出了各种各样的数字实验,以说明微量微量图的质和量特征以及相关的离散问题。