L²-estimate for the discrete Plateau Problem
Date
2003-12-22
Authors
Pozzi, Paola
Journal Title
Journal ISSN
Volume Title
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
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Source
Mathematics of Computation
Type
Journal article