Barrett, John W. and Garcke, Harald and Nuernberg, Robert (2006) Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid. MATHEMATICS OF COMPUTATION, 75 (253): PII S0025-. pp. 7-41. ISSN 0025-5718,
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We consider a fully practical finite element approximation of the degenerate Cahn-Hilliard equation with elasticity: Find the conserved order parameter, theta(x, t) is an element of [-1, 1], and the displacement field, (u) under bar (x, t) is an element of R-2, such that [GRAPHICS] subject to an initial condition theta(0)(center dot) is an element of [-1, 1] on theta and boundary conditions on both equations. Here gamma is an element of R->0 is the interfacial parameter, Psi is a non-smooth double well potential, (epsilon) double under bar is the symmetric strain tensor, C is the possibly anisotropic elasticity tensor, c(s) := c(0) + 1/2 (1 - c(0)) (1 + s) with c(0)(gamma) is an element of R->0 and b(s) := 1 - s(2) is the degenerate diffusional 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | DEGENERATE PARABOLIC EQUATION; LUBRICATION-TYPE EQUATIONS; CAHN-HILLIARD EQUATION; THIN-FILM; INTERFACE MODEL; ELECTROMIGRATION; SCHEMES; SINGULARITIES; CONVERGENCE; ELASTICITY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Mar 2021 07:25 |
| Last Modified: | 03 Mar 2021 07:25 |
| URI: | https://pred.uni-regensburg.de/id/eprint/35223 |
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