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The discrete Douglas problem: theory and numerics

Pozzi, Paola

Description

We solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating annulus-like, possibly unstable, minimal surfaces. In this paper we introduce the general framework, some preliminary estimates, develop the ideas used for the algorithm, and give the numerical results. Similarities and differences with respect to the fully discrete finite element procedure given by G. Dziuk and J. Hutchinson in the case of the classical Plateau problem are also...[Show more]

dc.contributor.authorPozzi, Paola
dc.date.accessioned2015-12-13T22:53:00Z
dc.date.available2015-12-13T22:53:00Z
dc.identifier.issn1463-9963
dc.identifier.urihttp://hdl.handle.net/1885/81643
dc.description.abstractWe solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating annulus-like, possibly unstable, minimal surfaces. In this paper we introduce the general framework, some preliminary estimates, develop the ideas used for the algorithm, and give the numerical results. Similarities and differences with respect to the fully discrete finite element procedure given by G. Dziuk and J. Hutchinson in the case of the classical Plateau problem are also addressed. In a subsequent paper we prove convergence estimates.
dc.publisherEuropean Mathematical Society Publishing House
dc.sourceInterfaces and Free Boundaries
dc.subjectKeywords: Douglas problem; Finite elements; Minimal surfaces; Order of convergence
dc.titleThe discrete Douglas problem: theory and numerics
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume6
dc.date.issued2004
local.identifier.absfor010106 - Lie Groups, Harmonic and Fourier Analysis
local.identifier.ariespublicationMigratedxPub9934
local.type.statusPublished Version
local.contributor.affiliationPozzi, Paola, College of Physical and Mathematical Sciences, ANU
local.bibliographicCitation.issue2
local.bibliographicCitation.startpage219
local.bibliographicCitation.lastpage252
dc.date.updated2015-12-11T10:53:34Z
local.identifier.scopusID2-s2.0-3242759059
CollectionsANU Research Publications

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