An r-adaptive finite element method for the solution of the two-dimensional phase-field equations

Beckett, G. and MacKenzie, John and Robertson, M.L. (2006) An r-adaptive finite element method for the solution of the two-dimensional phase-field equations. Communications in Computational Physics, 1 (5). pp. 805-826. ISSN 1815-2406

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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 discretised by a Calerkin finite element method. An adaptivity criterion is used that ensures that the mesh spacing at the phase front scales with the diffuse interface thickness.

ORCID iDs

Beckett, G., MacKenzie, John ORCID logoORCID: https://orcid.org/0000-0003-4412-7057 and Robertson, M.L.;