The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Interfaces and Free Boundaries


Full-Text PDF (1676 KB) | Metadata | Table of Contents | IFB summary
Volume 5, Issue 2, 2003, pp. 103–128
DOI: 10.4171/IFB/74

Published online: 2003-06-30

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

Erik Burman[1] and Marco Picasso[2]

(1) Ecole Polytechnique Fédérale de Lausanne, Switzerland
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland

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.

Keywords: adaptive finite elements; solutal dendrite

Burman Erik, Picasso Marco: Anisotropic, adaptative finite elements for the computation of a solutal dendrite. Interfaces Free Bound. 5 (2003), 103-128. doi: 10.4171/IFB/74