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Volume 1, Issue 5
An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations

G. Beckett, J. A. Mackenzie & M. L. Robertson

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

Published online: 2006-01

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  • 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 discretized 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.

  • Keywords

Phase change phase-field equidistribution moving meshes adaptive method.

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COPYRIGHT: © Global Science Press

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@Article{CiCP-1-805, author = {G. Beckett, J. A. Mackenzie and M. L. Robertson}, title = {An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations}, journal = {Communications in Computational Physics}, year = {2006}, volume = {1}, number = {5}, pages = {805--826}, 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 discretized 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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7980.html} }
TY - JOUR T1 - An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations AU - G. Beckett, J. A. Mackenzie & M. L. Robertson JO - Communications in Computational Physics VL - 5 SP - 805 EP - 826 PY - 2006 DA - 2006/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7980.html KW - Phase change KW - phase-field KW - equidistribution KW - moving meshes KW - adaptive method. AB -

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 discretized 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.

G. Beckett, J. A. Mackenzie and M. L. Robertson. (2006). An r-Adaptive Finite Element Method for the Solution of the Two-Dimensional Phase-Field Equations. Communications in Computational Physics. 1 (5). 805-826. doi:
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