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Anisotropic, adaptive finite elements for the computation of a solutal dendrite
journal contribution
posted on 2023-06-08, 07:27 authored by Erik Burman, Marco PicassoWe 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.
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Publication status
- Published
Journal
Interfaces and Free BoundariesISSN
1463-9963Publisher
European Mathematical SocietyExternal DOI
Issue
2Volume
5Page range
103-127Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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