𝐿²-estimate for the discrete Plateau Problem

Pozzi, Paola

doi:10.1090/S0025-5718-03-01630-2

$L^2$-estimate for the discrete Plateau Problem
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Math. Comp. 73 (2004), 1763-1777 Request permission

Abstract:

In this paper we prove the $L^2$ convergence rates for a fully discrete finite element procedure for approximating minimal, possibly unstable, surfaces.

Originally this problem was studied by G. Dziuk and J. Hutchinson. First they provided convergence rates in the $H^1$ and $L^2$ norms for the boundary integral method. Subsequently they obtained the $H^1$ convergence estimates using a fully discrete finite element method. We use the latter framework for our investigation.

References

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Gerhard Dziuk and John E. Hutchinson, The discrete Plateau problem: convergence results, Math. Comp. 68 (1999), no. 226, 519–546. MR 1613699, DOI 10.1090/S0025-5718-99-01026-1
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