Garcke, Harald and Weikard, Ulrich (2005) Numerical approximation of the Cahn-Larche equation. NUMERISCHE MATHEMATIK, 100 (4). pp. 639-662. ISSN 0029-599X, 0945-3245
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Spinodal decomposition, i.e., the separation of a homogeneous mixture into different phases, can be modeled by the Cahn-Hilliard equation - a fourth order semilinear parabolic equation. If elastic stresses due to a lattice misfit become important, the Cahn-Hilliard equation has to be coupled to an elasticity system to take this into account. Here, we present a discretization based on finite elements and an implicit Euler scheme. We first show solvability and uniqueness of solutions. Based on an energy decay property we then prove convergence of the scheme. Finally we present numerical experiments showing the impact of elasticity on the morphology of the microstructure.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HILLIARD EQUATION; PHASE-SEPARATION; GINZBURG-LANDAU; SOLIDS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 May 2021 09:49 |
| Last Modified: | 11 May 2021 09:49 |
| URI: | https://pred.uni-regensburg.de/id/eprint/36093 |
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