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Goal‐oriented adaptive refinement for phase field modeling with finite elements
Author(s) -
Mahnken R.
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4464
Subject(s) - polygon mesh , finite element method , mathematics , tangent , finite difference , field (mathematics) , nonlinear system , phase (matter) , transformation (genetics) , computer science , grid , adaptive mesh refinement , finite difference method , mathematical optimization , mathematical analysis , geometry , computational science , physics , biochemistry , chemistry , quantum mechanics , gene , pure mathematics , thermodynamics
SUMMARY Phase field modeling is very often performed with the finite‐difference method for equally spaced grids. Typically its solutions are highly non‐homogenous; and, therefore, non‐equally spaced grids with dense meshes at interfaces between different phases and coarse meshes in homogenous regions would be more advantageous with respect to both, efficiency and reliability of the numerical solutions. To this end, in the present work, an adaptive strategy with finite elements for phase field modeling is adopted, where the time step and the grid size are selected on the basis of goal‐oriented error estimation. In order to account for nonlinearity of the variational equations, we introduce a secant form for the dual problem, which for practical purposes is approximated by a tangent form. In a numerical example, we investigate transformation and retransformation for a two‐phase system in a square region subjected to thermal loading. Copyright © 2013 John Wiley & Sons, Ltd.