Barrett, John W. and Garcke, Harald and Nürnberg, Robert
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid.
Mathematics of Computation (MCOM) 75 (253), pp. 7-41.
We consider a fully practical finite element approximation of the degenerate Cahn-Hilliard equation with elasticity: Find the conserved order parameter, , and the displacement field, , such that = (b() [- + ^'() + 12 c' ()( u) : ( u)] ), (c() ()) = 0, subject to an initial condition on and boundary conditions on both equations. Here is the interfacial parameter, is a nonsmooth double well potential, is the symmetric strain tensor, is the possibly anisotropic elasticity tensor, with and is the degenerate diffusion mobility. In addition to showing stability bounds for our approximation, we prove convergence, and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions. Finally, some numerical experiments are presented.
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Primary 65M60, 65M12, 65M50, 35K55, 35K65, 35K35, 82C26, 74F15||MSC|
|Keywords:||degenerate Cahn-Hilliard equation; elasticity; convergence; nonlinear degenerate parabolic system|
|Subjects:||500 Science > 510 Mathematics|
|Created at the University of Regensburg:||Unknown|
|Deposited On:||27 Nov 2009 06:50|
|Last Modified:||20 Jul 2011 22:08|