Numerical Analysis of the Plateau Problem by the Method of Fundamental Solutions

Toward 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 \(L^\infty \) $L^{\infty }$ -error analysis for mean curvature. Each of the approximate solutions in our scheme is a smooth surface, a significant difference from previous studies that required mesh generation.