Published

Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: Methods and Error Analysis

Wansheng Wang, Long Chen, and Jie Zhou

Journal of Scientific Computin, 67 (2), 724 - 746, 2016.

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ABSTRACT:

 A postprocessing technique for mixed finite element methods
for the Cahn-Hilliard equation is developed and analyzed. Once the
mixed finite element approximations have been computed at a fixed time
on the coarser mesh, the approximations are postprocessed by solving
two decoupled Poisson equations in an enriched finite element space
(either on a finer grid or a higher-order space) for which many fast
Poisson solvers can be applied. The nonlinear iteration is only
applied to a much smaller size problem and the computational cost
using Newton and direct solvers is negligible compared with the cost
of the linear problem. The analysis presented here shows that this
technique remains the optimal rate of convergence for both the
concentration and the chemical potential approximations.