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A second order splitting method for the Cahn-Hilliard equation

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Summary

A semi-discrete finite element method requiring only continuous element is presented for the approximation of the solution of the evolutionary, fourth order in space, Cahn-Hilliard equation. Optimal order error bounds are derived in various norms for an implementation which uses mass lumping. The continuous problem has an energy based Lyapunov functional. It is proved that this property holds for the discrete problem.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Sussex, BN1 9QH, Brighton, UK

    C. M. Elliott

  2. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    D. A. French

  3. Department of Mathematics, Purdue University, 4790, West Lafayette, IN, USA

    F. A. Milner

Authors
  1. C. M. Elliott
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  2. D. A. French
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  3. F. A. Milner
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Additional information

Research partially supported by NSF Grant DMS-8896141

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Elliott, C.M., French, D.A. & Milner, F.A. A second order splitting method for the Cahn-Hilliard equation. Numer. Math. 54, 575–590 (1989). https://doi.org/10.1007/BF01396363

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  • DOI: https://doi.org/10.1007/BF01396363

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