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Research Report MRR01-018

L2-Estimate for the Discrete Plateau Problem

Paola Pozzi

Abstract: In the articles [1], [2], [3], [4], the authors J. Hutchinson and G. Dziuk solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating minimal, including unstable, surfaces.
In the first two papers, they prove convergence rates in the H1 and L2 norms for the boundary integral method. In the subsequent two articles [3] and [4] they obtain the H1 convergence estimates using a fully discrete finite element method.
Here I want to prove the L2 convergence rates for the fully discrete method. The set up will be the one defined in [3].

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