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

G. Beckett, John MacKenzie, M.L. Robertson

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)805-826
Number of pages22
JournalCommunications in Computational Physics
Issue number5
Publication statusPublished - 2006


  • phase change
  • phase-field
  • equidistribution
  • moving meshes
  • adaptive method

Cite this