L²-estimate for the discrete Plateau Problem

Date

2003-12-22

Authors

Pozzi, Paola

Journal Title

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Publisher

American Mathematical Society

Abstract

In this paper we prove the L² convergence rates for a fully discrete finite element procedure for approximating minimal, possibly unstable, surfaces. Originally this problem was studied by G. Dziuk and J. Hutchinson. First they provided convergence rates in the H¹ and L² norms for the boundary integral method. Subsequently they obtained the H¹ convergence estimates using a fully discrete finite element method. We use the latter framework for our investigation.

Description

Keywords

Minimal surfaces, finite elements, order of convergence, Plateau Problem

Citation

Source

Mathematics of Computation

Type

Journal article

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