- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:02
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2003
2
Anisotropic, adaptative finite elements for the computation of a solutal dendrite
Erik
Burman
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
Marco
Picasso
Ecole Polytechnique Fédérale de Lausanne, LAUSANNE, SWITZERLAND
adaptive finite elements; solutal dendrite
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.
Functional analysis
General
103
128
10.4171/IFB/74
http://www.ems-ph.org/doi/10.4171/IFB/74