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A posteriori estimates for the Cahn-Hilliard equation with obstacle free energy. (English) Zbl 1190.65137
This paper deals with the Cahn-Hilliard equation with a double obstacle potential (as an energy potential). The authors consider the system of elliptic variational equality and inequality resulting from a backward Euler discretization of the time variable for the Cahn-Hilliard equation. They study the piecewise linear finite element approximation and derive several a posteriori estimates with a localized interior residual. Then, they propose mesh adaption algorithms for the time-dependent problems based on a posteriori estimations. Robustness and efficiency of those algorithms are well confirmed by numerical experiments in two and three dimensional space dimensions.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators
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