Anisotropic, adaptive finite elements for the computation of a solutal dendrite

Burman, Erik and Picasso, Marco (2003) Anisotropic, adaptive finite elements for the computation of a solutal dendrite. Interfaces and Free Boundaries, 5 (2). pp. 103-127. ISSN 1463-9963

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Abstract

We compute solutions of solutal phase-field models for dendritic growth of an isothermal binary alloy using anisotropic mesh refinement techniques. The adaptive strategy is based on anisotropic a posteriori estimators using a superconvergent recovery technique in the form of the Zienkiewicz-Zhu error estimator. The phase-field model contains an anisotropic strongly nonlinear second order operator modelling the dendritic branches, this strong nonlinearity is included in the a posteriori error estimators by using a monotonicity result. The monotonicity holds for phase-field anisotropy below a certain threshold value beyond which there are no known well-posedness results. We present computational results for both regimes showing the performance of the proposed method.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 20:42
Last Modified: 27 Apr 2012 08:34
URI: http://sro.sussex.ac.uk/id/eprint/27608
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