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.

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 - Jan 2011
Externally published	Yes

Bibliographical 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.

Keywords

Cahn-Hilliard
a posteriori error estimation
diffuse interface
dual Cahn-Hilliard
dual well-posedness
error-residual equivalence
goal-oriented error analysis
linearized adjoint
quantities of interest

ASJC Scopus subject areas

Computational Mathematics
Analysis
Applied Mathematics
Numerical Analysis

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10.1002/num.20638

Cite this

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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.",

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doi = "10.1002/num.20638",

language = "English (US)",

volume = "27",

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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.

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KW - dual Cahn-Hilliard

KW - dual well-posedness

KW - error-residual equivalence

KW - goal-oriented error analysis

KW - linearized adjoint

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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