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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 Picasso
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.

History

Publication status

  • Published

Journal

Interfaces and Free Boundaries

ISSN

1463-9963

Publisher

European Mathematical Society

Issue

2

Volume

5

Page range

103-127

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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