Numerische Mathematik

, Volume 54, Issue 5, pp 575–590

A second order splitting method for the Cahn-Hilliard equation

  • C. M. Elliott
  • D. A. French
  • F. A. Milner

DOI: 10.1007/BF01396363

Cite this article as:
Elliott, C.M., French, D.A. & Milner, F.A. Numer. Math. (1989) 54: 575. doi:10.1007/BF01396363


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.

Subject Classifications

AMS(MOS): 65N30 CR: G1.8 

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • C. M. Elliott
    • 1
  • D. A. French
    • 2
  • F. A. Milner
    • 3
  1. 1.School of Mathematical and Physical SciencesUniversity of SussexBrightonUK
  2. 2.Department of MathematicsCarnegie-Mellon UniversityPittsburghUSA
  3. 3.Department of MathematicsPurdue UniversityWest LafayetteUSA

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