Geodesic
Computational studies of anisotropic diffuse interface model of microstructure formation in solidification
Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 1 
M. Benes. Computational studies of anisotropic diffuse interface model of microstructure formation  in solidification. Acta mathematica Universitatis Comenianae, Tome 76 (2007) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2007_76_1_a3/
@article{AMUC_2007_76_1_a3,
     author = {M. Benes},
     title = {Computational studies of anisotropic diffuse interface model of microstructure formation  in solidification},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2007},
     volume = {76},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2007_76_1_a3/}
}
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%J Acta mathematica Universitatis Comenianae
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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.