A second order splitting method for the Cahn-Hilliard equation

C. M. Elliott, D. A. French, Fabio Milner

Research output: Contribution to journalArticle

159 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)575-590
Number of pages16
JournalNumerische Mathematik
Volume54
Issue number5
DOIs
StatePublished - Sep 1989
Externally publishedYes

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Cahn-Hilliard Equation
Splitting Method
Mass Lumping
Finite element method
Lyapunov Functional
Error Bounds
Fourth Order
Finite Element Method
Norm
Approximation
Energy

Keywords

  • Subject Classifications: AMS(MOS): 65N30, CR: G1.8

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Mathematics(all)

Cite this

A second order splitting method for the Cahn-Hilliard equation. / Elliott, C. M.; French, D. A.; Milner, Fabio.

In: Numerische Mathematik, Vol. 54, No. 5, 09.1989, p. 575-590.

Research output: Contribution to journalArticle

Elliott, C. M. ; French, D. A. ; Milner, Fabio. / A second order splitting method for the Cahn-Hilliard equation. In: Numerische Mathematik. 1989 ; Vol. 54, No. 5. pp. 575-590.
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