L2-estimate for the discrete plateau problem

Paola Pozzi

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

L²-estimate for the discrete plateau problem

Paola Pozzi^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

In this paper we prove the L² 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 H¹ and L² 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.

Original language	English
Pages (from-to)	1763-1777
Number of pages	15
Journal	Mathematics of Computation
Volume	73
Issue number	248
DOIs	https://doi.org/10.1090/S0025-5718-03-01630-2
Publication status	Published - Oct 2004

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title = "L2-estimate for the discrete plateau problem",

abstract = "In this paper we prove the L2 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 H1 and L2 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.",

keywords = "Finite elements, Minimal surfaces, Order of convergence, Plateau Problem",

author = "Paola Pozzi",

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PY - 2004/10

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N2 - In this paper we prove the L2 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 H1 and L2 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.

AB - In this paper we prove the L2 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 H1 and L2 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.

KW - Finite elements

KW - Minimal surfaces

KW - Order of convergence

KW - Plateau Problem

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U2 - 10.1090/S0025-5718-03-01630-2

DO - 10.1090/S0025-5718-03-01630-2

M3 - Article

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VL - 73

SP - 1763

EP - 1777

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 248

ER -

L²-estimate for the discrete plateau problem

Abstract

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