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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: John W. Barrett and James F. Blowey
Journal: Math. Comp. 68 (1999), 487-517
MSC (1991): Primary 65M60, 65M15, 35K55, 35K35, 82C26
MathSciNet review: 1609678
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

John W. Barrett
Affiliation: Department of Mathematics, Imperial College, London SW7 2BZ, U.K.
Email: j.barrett@ic.ac.uk

James F. Blowey
Affiliation: Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, U.K.
Email: j.f.blowey@durham.ac.uk

DOI: http://dx.doi.org/10.1090/S0025-5718-99-01015-7
PII: S 0025-5718(99)01015-7
Received by editor(s): July 16, 1996
Received by editor(s) in revised form: September 16, 1997
Article copyright: © Copyright 1999 American Mathematical Society