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

Kristoffer G. van der Zee; J. Tinsley Oden; Serge Prudhomme; Andrea Hawkins-Daarud

doi:10.1002/num.20638

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

Kristoffer G. van der Zee, J. Tinsley Oden, Serge Prudhomme, Andrea Hawkins-Daarud

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

26 Scopus citations

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.

Original language	English (US)
Pages (from-to)	160-196
Number of pages	37
Journal	Numerical Methods for Partial Differential Equations
Volume	27
Issue number	1
DOIs	https://doi.org/10.1002/num.20638
State	Published - Oct 27 2010
Externally published	Yes

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title = "Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition",

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. {\textcopyright} 2010 Wiley Periodicals, Inc.",

author = "{van der Zee}, {Kristoffer G.} and {Tinsley Oden}, J. and Serge Prudhomme and Andrea Hawkins-Daarud",

note = "KAUST Repository Item: Exported on 2020-04-23 Acknowledged KAUST grant number(s): US00003 Acknowledgements: Contract grant sponsor: DOE Multiscale Mathematics; contract grant number: DE-FG02-05ER25701Contract grant sponsor: KAUST; contract grant number: US00003 This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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doi = "10.1002/num.20638",

language = "English (US)",

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AU - van der Zee, Kristoffer G.

AU - Tinsley Oden, J.

AU - Prudhomme, Serge

AU - Hawkins-Daarud, Andrea

N1 - KAUST Repository Item: Exported on 2020-04-23 Acknowledged KAUST grant number(s): US00003 Acknowledgements: Contract grant sponsor: DOE Multiscale Mathematics; contract grant number: DE-FG02-05ER25701Contract grant sponsor: KAUST; contract grant number: US00003 This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2010/10/27

Y1 - 2010/10/27

N2 - 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.

AB - 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.

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DO - 10.1002/num.20638

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JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 1

ER -

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

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