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Towards identifying the number of minimal surfaces sharing the same boundaryfrom the geometry of the boundary, we propose a numerical scheme with highspeed and high accuracy. Our numerical scheme is based on the method offundamental solutions. We establish the convergence analysis for Dirichletenergy and $L^\infty$-error analysis for mean curvature. Each of theapproximate solutions in our scheme is a smooth surface, which is a significantdifference from previous studies that required mesh division.

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