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.
1
Ecole Polytechnique Fédérale de Lausanne, Switzerland
Erik Burman; Marco Picasso. Anisotropic, adaptative finite elements for the computation of a solutal dendrite. Interfaces and free boundaries, Tome 5 (2003) no. 2, pp. 103-128. doi: 10.4171/ifb/74
@article{10_4171_ifb_74,
author = {Erik Burman and Marco Picasso},
title = {Anisotropic, adaptative finite elements for the computation of a solutal dendrite},
journal = {Interfaces and free boundaries},
pages = {103--128},
year = {2003},
volume = {5},
number = {2},
doi = {10.4171/ifb/74},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/74/}
}
TY - JOUR
AU - Erik Burman
AU - Marco Picasso
TI - Anisotropic, adaptative finite elements for the computation of a solutal dendrite
JO - Interfaces and free boundaries
PY - 2003
SP - 103
EP - 128
VL - 5
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/74/
DO - 10.4171/ifb/74
ID - 10_4171_ifb_74
ER -
%0 Journal Article
%A Erik Burman
%A Marco Picasso
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%J Interfaces and free boundaries
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%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/74/
%R 10.4171/ifb/74
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