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

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 e...

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Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Sakakibara, Koya, Shimizu, Yuuki
Format: Article
Language:English
Subjects:
Dirichlet problem
Error analysis
Minimal surfaces
Numerical analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422