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 en...

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Bibliographic Details
Published in:	Journal of scientific computing Vol. 100; no. 1; p. 2
Main Authors:	Sakakibara, Koya, Shimizu, Yuuki
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-07-2024 Springer Nature B.V
Subjects:	Algorithms Approximation Boundary value problems Computational Mathematics and Numerical Analysis Dirichlet problem Error analysis Finite element analysis Finite volume method Geometry Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Mesh generation Minimal surfaces Numerical analysis Optimization Theoretical 53A10 65N35 65N80 Method of fundamental solutions Plateau problem 65K10 Minimal surface
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Summary:	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 ∞ -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.
ISSN:	0885-7474 1573-7691
DOI:	10.1007/s10915-024-02551-z