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$L^2$-estimate for the discrete Plateau Problem

Author: Paola Pozzi
Translated by:
Journal: Math. Comp. 73 (2004), 1763-1777
MSC (2000): Primary 65N30; Secondary 49Q05, 53A10
Published electronically: December 22, 2003
MathSciNet review: 2059735
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Abstract: In this paper we prove the $L^2$ 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 $H^1$ and $L^2$ norms for the boundary integral method. Subsequently they obtained the $H^1$ convergence estimates using a fully discrete finite element method. We use the latter framework for our investigation.

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Additional Information

Paola Pozzi
Affiliation: Centre for Mathematics and its Applications, MSI, Australian National University, Canberra, Australian Capital Territory 0200, Australia

Keywords: Minimal surfaces, finite elements, order of convergence, Plateau Problem
Received by editor(s): June 12, 2002
Received by editor(s) in revised form: March 11, 2003
Published electronically: December 22, 2003
Article copyright: © Copyright 2003 American Mathematical Society