Numerical analysis for the Plateau problem by the method of fundamental solutions

Abstract: Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental solutions. We establish the convergence analysis for Dirichlet energy and $L^\infty$-error analysis for mean curvature. Each of the approximate solutions in our scheme is a smooth surface, which is a significant difference from previous studies that required mesh division.