Commun. Comput. Phys., 1 (2006), pp. 805-826.


An $r$-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations

G. Beckett, 1, J. A. Mackenzie 1*, M. L. Robertson 1

1 Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland.

Received 17 October 2005; Accepted (in revised version) 6 February 2006

Abstract

An adaptive moving mesh method is developed for the numerical solution of two-dimensional phase change problems modelled by the phase-field equations. The numerical algorithm is relatively simple and is shown to be more efficient than fixed grid methods. The phase-field equations are discretised by a Galerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.


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Key words: Phase change; phase-field; equidistribution; moving meshes; adaptive method.


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Correspondence to: J. A. Mackenzie , Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, Scotland. Email: jam@maths.strath.ac.uk
 

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