The Finite Element Approximation for Minimal Surfaces Subject to the Plateau Problems

摘要

This paper talks about generating the minimal surfaces which are subject to the wellknownrnPlateau problem. The differential form of the Plateau problem is deu0002ned atrnu0002rst and, its associated discrete schemes which reduced from the u0002nite element methodsrncould be practically solved by the numerical iteration methods like the Newton'srniteration. The convergence property of the u0002nite element solutions are proved by stepsrnand some multi-grid algorithms have been implemented to speed up the computation.rnThese new approximation methods will be applied to the project of generating thernminimal surfaces on computer softwares later.