Summary
A solutal, anisotropic phase-field model for dendritic growth of an isothermal binary alloy is considered. Existence of a weak solution is established provided the physical anisotropy is small enough. A semi-implicit finite element method is proposed to solve the problem. A priori and a posteriori error estimates are derived when the physical anisotropy is small. An adaptive algorithm which aims at producing meshes with large aspect ratio is proposed. Numerical results show that accurate solutions can be obtained, even when the physical anisotropy is large.
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Burman, E., Picasso, M., Rappaz, J. (2004). Analysis and Computation of Dendritic Growth in Binary Alloys Using a Phase-Field Model. In: Feistauer, M., Dolejší, V., Knobloch, P., Najzar, K. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18775-9_18
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DOI: https://doi.org/10.1007/978-3-642-18775-9_18
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