Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition

Handle URI:
http://hdl.handle.net/10754/598419
Title:
Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition
Authors:
van der Zee, Kristoffer G.; Tinsley Oden, J.; Prudhomme, Serge; Hawkins-Daarud, Andrea
Abstract:
A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two-dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc.
Citation:
Van der Zee KG, Tinsley Oden J, Prudhomme S, Hawkins-Daarud A (2010) Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition. Numerical Methods for Partial Differential Equations 27: 160–196. Available: http://dx.doi.org/10.1002/num.20638.
Publisher:
Wiley-Blackwell
Journal:
Numerical Methods for Partial Differential Equations
KAUST Grant Number:
US00003
Issue Date:
27-Oct-2010
DOI:
10.1002/num.20638
Type:
Article
ISSN:
0749-159X
Sponsors:
Contract grant sponsor: DOE Multiscale Mathematics; contract grant number: DE-FG02-05ER25701Contract grant sponsor: KAUST; contract grant number: US00003
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorvan der Zee, Kristoffer G.en
dc.contributor.authorTinsley Oden, J.en
dc.contributor.authorPrudhomme, Sergeen
dc.contributor.authorHawkins-Daarud, Andreaen
dc.date.accessioned2016-02-25T13:20:24Zen
dc.date.available2016-02-25T13:20:24Zen
dc.date.issued2010-10-27en
dc.identifier.citationVan der Zee KG, Tinsley Oden J, Prudhomme S, Hawkins-Daarud A (2010) Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition. Numerical Methods for Partial Differential Equations 27: 160–196. Available: http://dx.doi.org/10.1002/num.20638.en
dc.identifier.issn0749-159Xen
dc.identifier.doi10.1002/num.20638en
dc.identifier.urihttp://hdl.handle.net/10754/598419en
dc.description.abstractA posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two-dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc.en
dc.description.sponsorshipContract grant sponsor: DOE Multiscale Mathematics; contract grant number: DE-FG02-05ER25701Contract grant sponsor: KAUST; contract grant number: US00003en
dc.publisherWiley-Blackwellen
dc.subjecta posteriori error estimationen
dc.subjectCahn-Hilliarden
dc.subjectdiffuse interfaceen
dc.subjectdual Cahn-Hilliarden
dc.subjectdual well-posednessen
dc.subjecterror-residual equivalenceen
dc.subjectgoal-oriented error analysisen
dc.subjectlinearized adjointen
dc.subjectquantities of interesten
dc.titleGoal-oriented error estimation for Cahn-Hilliard models of binary phase transitionen
dc.typeArticleen
dc.identifier.journalNumerical Methods for Partial Differential Equationsen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
kaust.grant.numberUS00003en
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