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Unconditionally Gradient Stable Time Marching the Cahn-Hilliard Equation

  • David J. Eyre (a1)

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.

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

Unconditionally Gradient Stable Time Marching the Cahn-Hilliard Equation

  • David J. Eyre (a1)

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