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

K.G. Zee, van der, J.T. Oden, S. Prudhomme, A. Hawkins-Daarud

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    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 languageEnglish
    Pages (from-to)160-196
    JournalNumerical Methods for Partial Differential Equations
    Volume27
    Issue number1
    DOIs
    Publication statusPublished - 2010

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