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L²-estimate for the discrete Plateau Problem

Pozzi, Paola

Description

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 H¹ convergence estimates using a fully discrete finite element method. We use the latter framework for our investigation.

dc.contributor.authorPozzi, Paola
dc.date.accessioned2016-03-15T05:31:51Z
dc.date.available2016-03-15T05:31:51Z
dc.identifier.issn0025-5718
dc.identifier.urihttp://hdl.handle.net/1885/100253
dc.description.abstractIn 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 H¹ convergence estimates using a fully discrete finite element method. We use the latter framework for our investigation.
dc.publisherAmerican Mathematical Society
dc.rights© 2003 American Mathematical Society
dc.sourceMathematics of Computation
dc.subjectMinimal surfaces
dc.subjectfinite elements
dc.subjectorder of convergence
dc.subjectPlateau Problem
dc.titleL²-estimate for the discrete Plateau Problem
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume73
dc.date.issued2003-12-22
local.identifier.absfor010399
local.identifier.ariespublicationMigratedxPub7303
local.publisher.urlhttp://www.ams.org/journals/
local.type.statusPublished Version
local.contributor.affiliationPozzi, Paola, College of Physical and Mathematical Sciences, CPMS Mathematical Sciences Institute, Centre for Mathematics and Its Applications, The Australian National University
local.bibliographicCitation.issue248
local.bibliographicCitation.startpage1763
local.bibliographicCitation.lastpage1778
local.identifier.doi10.1090/S0025-5718-03-01630-2
dc.date.updated2016-06-14T08:37:27Z
local.identifier.scopusID2-s2.0-5644227596
CollectionsANU Research Publications

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