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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The discrete plateau problem: Convergence results
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by Gerhard Dziuk and John E. Hutchinson PDF
Math. Comp. 68 (1999), 519-546 Request permission

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
  • MR Author ID: 90330
  • Email: John.Hutchinson@anu.edu.au
  • Received by editor(s): August 26, 1996
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 519-546
  • MSC (1991): Primary 65N30; Secondary 49Q05, 53A10
  • DOI: https://doi.org/10.1090/S0025-5718-99-01026-1
  • MathSciNet review: 1613699