Finite element discretizations of nonlocal minimal graphs: Convergence

In this paper, we propose and analyze a finite element discretization for the computation of fractional minimal graphs of order~$s \in (0,1/2)$ on a bounded domain $\Omega$. Such a Plateau problem of order $s$ can be reinterpreted as a Dirichlet problem for a nonlocal, nonlinear, degenerate operator of order $s + 1/2$. We prove that our numerical scheme converges in $W^{2r}_1(\Omega)$ for all $r
Comment: Lemma 4.1 was removed due to a mistake in its proof. This only affects the new Theorem 4.2 (convergence), whose proof has been corrected