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

2022/12/13 by Koya Sakakibara, Sakakibara, Koya, Yuuki Shimizu +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2212.06508

openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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^∞-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.

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