Convergence of the finite element method applied to an anisotropic phase-field model
Burman, Erik1 ; Kessler, Daniel2 ; Rappaz, Jacques1
1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland
2 University of Maryland Department of Mathematics College Park MD 20740 USA
Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 1, pp. 67-94.

We formulate a finite element method for the computation of solutions to an anisotropic phase-field model for a binary alloy. Convergence is proved in the H 1 -norm. The convergence result holds for anisotropy below a certain threshold value. We present some numerical experiments verifying the theoretical results. For anisotropy below the threshold value we observe optimal order convergence, whereas in the case where the anisotropy is strong the numerical solution to the phase-field equation does not converge.

DOI : 10.5802/ambp.186
Burman, Erik 1 ; Kessler, Daniel 2 ; Rappaz, Jacques 1

1 Ecole Polytechnique Federale Institute of Analysis and Scientific Computing CH-1015 Lausanne Switzerland
2 University of Maryland Department of Mathematics College Park MD 20740 USA 
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Burman, Erik; Kessler, Daniel; Rappaz, Jacques. Convergence of the finite element method applied to an anisotropic phase-field model. Annales mathématiques Blaise Pascal, Tome 11 (2004) no. 1, pp. 67-94. doi : 10.5802/ambp.186. http://www.numdam.org/articles/10.5802/ambp.186/

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