ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXVI, 1 (2007)
p. 39 - 50
Computational studies of anisotropic diffuse interface model of microstructure formation in solidification
M. Benes

Abstract.  The growth of microstructure non-convex patterns is studied by means of the modified anisotropic phase-field model. The numerical algorithm is designed using the finite-difference spatial discretisation in the method of lines. Results of numerical analysis of the model are based on the a-priori estimates, the compactness and monotonicity arguments. As a quantitative result, we present the convergence studies of the dendritic growth when the mesh size and the diffuse parameter tend to zero.

Keywords.  Phase-field method, finite-difference method, monotonicity method, dendritic growth.

AMS Subject classification.  Primary: 80A22, 82C26, 35A40.
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Acta Mathematica Universitatis Comenianae
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