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

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.


Published in:
Interfaces and Free Boundaries, 5, 2, 103-127
Year:
2003
ISSN:
1463-9971
Keywords:
Note:
Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland. Burman, E, Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland. ISI Document Delivery No.: 687WF Times Cited: 1 Cited Reference Count: 25
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 Record created 2006-08-24, last modified 2018-03-18


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