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An r-adaptive finite element method for the solution of the two-dimensional phase-field equations
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2006
Year
Numerical AnalysisFinite Element MethodMesh OptimizationMethod Of Fundamental SolutionEngineeringDiffuse Interface ThicknessSemi-implicit MethodMechanical EngineeringNumerical SimulationAdaptivity CriterionComputational ElectromagneticsTwo-dimensional Phase-field EquationsComputational MechanicsUnstructured Mesh GenerationBoundary Element MethodMesh SpacingNumerical Method For Partial Differential EquationMultiscale Modeling
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.