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

Authors
Barrett, JW Blowey, JF
Citation
Jw. Barrett et Jf. Blowey, Finite element approximation of the Cahn-Hilliard equation with concentration dependent mobility, MATH COMPUT, 68(226), 1999, pp. 487-517
Citations number
19
Categorie Soggetti
Mathematics
Journal title
MATHEMATICS OF COMPUTATION
ISSN journal
00255718 → ACNP
Volume
68
Issue
226
Year of publication
1999
Pages
487 - 517
Database
ISI
SICI code
0025-5718(199904)68:226<487:FEAOTC>2.0.ZU;2-U
Abstract
We consider the Cahn-Hilliard equation with a logarithmic free energy and n on-degenerate concentration dependent mobility. In particular we prove that there exists a unique solution for sufficiently smooth initial data. Furth er, we prove an error bound for a fully practical piecewise linear finite e lement approximation in one and two space dimensions. Finally some numerica l experiments are presented.