JournalsifbVol. 5, No. 2pp. 103–128

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

  • Erik Burman

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
  • Marco Picasso

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
Anisotropic, adaptative finite elements for the computation of a solutal dendrite cover
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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.

Cite this article

Erik Burman, Marco Picasso, Anisotropic, adaptative finite elements for the computation of a solutal dendrite. Interfaces Free Bound. 5 (2003), no. 2, pp. 103–128

DOI 10.4171/IFB/74