Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-25T15:38:32.269Z Has data issue: false hasContentIssue false

Unconditionally Gradient Stable Time Marching the Cahn-Hilliard Equation

Published online by Cambridge University Press:  10 February 2011

David J. Eyre*
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, [email protected]
Get access

Abstract

Numerical methods for time stepping the Cahn-Hilliard equation are given and discussed. The methods are unconditionally gradient stable, and are uniquely solvable for all time steps. The schemes require the solution of ill-conditioned linear equations, and numerical methods to accurately solve these equations are also discussed.

Type
Research Article
Copyright
Copyright © Materials Research Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ames, W. F., Numerical Methods for Partial Differential Equations, Academic Press, New York (1977), pp. 304307.Google Scholar
[2] Cahn, J. W., Acta Met., 9 (1961), pp. 795801.Google Scholar
[3] Elliott, C. M., in Mathematical Models for Phase Change Problems, Rodrigues, J. F., ed., Birkhduser Verlag, Basel, 1989, pp. 3573.Google Scholar
[4] Eyre, D. J., preprint.Google Scholar
[5] Golub, G. and Loan, C. F. Van, Matrix Computations, Johns Hopkins Press, Baltimore (1983), pp. 353361.Google Scholar
[6] Sonneveld, P., SIAM J. Sci. Stat. Comput., 10 (1989), pp. 3652.Google Scholar
[7] Stuart, A. M. and Humphries, A. R., SIAM Rev., 36 (1994), pp. 226257.Google Scholar