The discrete Plateau Problem: Convergence results

Gerhard Dziuk; John E. Hutchinson

doi:10.1090/s0025-5718-99-01026-1

The discrete Plateau Problem: Convergence results

Gerhard Dziuk^*, John E. Hutchinson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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.

Original language	English
Pages (from-to)	519-546
Number of pages	28
Journal	Mathematics of Computation
Volume	68
Issue number	226
DOIs	https://doi.org/10.1090/s0025-5718-99-01026-1
Publication status	Published - Apr 1999

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title = "The discrete Plateau Problem: Convergence results",

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.",

keywords = "Finite elements, Minimal surface, Order of convergence, Plateau problem",

author = "Gerhard Dziuk and Hutchinson, {John E.}",

year = "1999",

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AU - Hutchinson, John E.

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AB - 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.

KW - Finite elements

KW - Minimal surface

KW - Order of convergence

KW - Plateau problem

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DO - 10.1090/s0025-5718-99-01026-1

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EP - 546

JO - Mathematics of Computation

JF - Mathematics of Computation

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The discrete Plateau Problem: Convergence results

Abstract

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