Published

An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation

Jie Zhou, Long Chen, Yunqing Huang and Wansheng Wang

Communications in Computational Physics. 17(01), 127-145, 2015.

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ABSTRACT:

 A two-grid method for solving the Cahn-Hilliard equation is
proposed in this paper. This two-grid method consists of two
steps. First, solve the Cahn-Hilliard equation with mixed finite
element on the coarse grid. Second, solve two Poisson equations using
multigrid methods on the fine grid. This two-grid method can also
combine with local mesh refinement to further improve the efficiency.
%We check the advantages of this method through several numerical
experiments including two and three dimension cases and using P1 and
P2 elements.  Numerical results including two and three dimension
cases with linear and quadratic elements show that this two-grid
method can speed up the existing mixed finite method while keeping the
same convergence rate.