Analysis of a finite element formulation for modelling phase separation
The Cahn-Hilliard equation is of importance in materials science and a range of other fields. It represents a diffuse interface model for simulating the evolution of phase separation in solids and fluids, and is a nonlinear fourth-order parabolic equation, which makes its numerical solution particularly challenging. To this end, a finite element formulation has been developed which can solve the Cahn-Hilliard equation in its primal form using C° basis functions. Here, analysis of a fully discrete version of this method is presented in the form of a priori uniqueness, stability and error analysis.
KeywordsCahn-Hilliard equation discontinuous Galerkin method phase separation.
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- 10.Engel G, Garikipati K, Hughes TJR, Larson MG, Mazzei L, Taylor RL (2002) Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with applications to thin beams and plates, and strain gradient elasticity. Computer Methods in Applied Mechanics and Engineering 191(34):3669–3750.MATHCrossRefMathSciNetGoogle Scholar