Interfaces and Free Boundaries
Full-Text PDF (1676 KB) | Metadata | Table of Contents | IFB summary
Published online: 2003-06-30
Anisotropic, adaptative finite elements for the computation of a solutal dendriteErik Burman and Marco Picasso (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