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2006-01-01Buch DOI: 10.18452/2748
A convergent adaptive finite element method for an optimal design problem
dc.contributor.authorBartels, Sören
dc.contributor.authorCarstensen, Carsten
dc.date.accessioned2017-06-15T18:10:30Z
dc.date.available2017-06-15T18:10:30Z
dc.date.created2006-09-13
dc.date.issued2006-01-01
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3400
dc.description.abstractAbstract. The optimal design problem for maximal torsion stiffness of an infinite bar of given geometry and unknown distribution of two materials of prescribed amounts is one model example in topology optimisation. It eventually leads to a degenerated convex minimisation problem. The numerical analysis is therefore delicate for possibly multiple primal variables $u$ but unique derivatives $\sigma := DW(Du)$. Even sharp a posteriori error estimates still suffer from the reliability-efficiency gap. However, it motivates a simple edgebased adaptive mesh-refining algorithm (AFEM) that is not a priori guaranteed to refine everywhere. Its convergence proof is therefore based on energy estimates and some refined convexity control. Numerical experiments illustrate even nearly optimal convergence rates of the proposed adaptive finite element method (AFEM).eng
dc.language.isoeng
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectconvergenceeng
dc.subjectadaptive algorithmeng
dc.subjectoptimal design problemeng
dc.subject.ddc510 Mathematik
dc.titleA convergent adaptive finite element method for an optimal design problem
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10068089
dc.identifier.doihttp://dx.doi.org/10.18452/2748
dc.subject.dnb27 Mathematik
local.edoc.pages29
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-year2006
dc.identifier.zdb2075199-0
bua.series.namePreprints aus dem Institut für Mathematik
bua.series.issuenumber2006,20

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