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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The discrete plateau problem:
Convergence results


Authors: Gerhard Dziuk and John E. Hutchinson
Journal: Math. Comp. 68 (1999), 519-546
MSC (1991): Primary 65N30; Secondary 49Q05, 53A10
MathSciNet review: 1613699
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Abstract: We solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating minimal, including unstable, surfaces. In a previous paper we introduced the general framework and some preliminary estimates, developed the algorithm and give the numerical results. In this paper we prove the convergence estimate.


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Additional Information

Gerhard Dziuk
Affiliation: Institut für Angewandte Mathematik, Universität Freiburg, Hermann–Herder–Str. 10, D-79104 Freiburg i. Br., GERMANY
Email: gerd@mathematik.uni-freiburg.de

John E. Hutchinson
Affiliation: Department of Mathematics, School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra, ACT 0200, AUSTRALIA
Email: John.Hutchinson@anu.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01026-1
PII: S 0025-5718(99)01026-1
Keywords: Minimal surface, finite elements, order of convergence, Plateau Problem
Received by editor(s): August 26, 1996
Article copyright: © Copyright 1999 American Mathematical Society