The discrete plateau problem: Convergence results

Dziuk, Gerhard; Hutchinson, John

doi:10.1090/S0025-5718-99-01026-1

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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