Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility

Barrett, John; Blowey, James

doi:10.1090/S0025-5718-99-01015-7

Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility
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by John W. Barrett and James F. Blowey PDF

Math. Comp. 68 (1999), 487-517 Request permission

Abstract:

We consider the Cahn-Hilliard equation with a logarithmic free energy and non-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Further, we prove an error bound for a fully practical piecewise linear finite element approximation in one and two space dimensions. Finally some numerical experiments are presented.

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