Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition

Feng, Xiaobing; Karakashian, Ohannes

doi:10.1090/S0025-5718-07-01985-0

Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition
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by Xiaobing Feng and Ohannes A. Karakashian PDF

Math. Comp. 76 (2007), 1093-1117 Request permission

Abstract:

Fully discrete discontinuous Galerkin methods with variable mesh- es in time are developed for the fourth order Cahn-Hilliard equation arising from phase transition in materials science. The methods are formulated and analyzed in both two and three dimensions, and are proved to give optimal order error bounds. This coupled with the flexibility of the methods demonstrates that the proposed discontinuous Galerkin methods indeed provide an efficient and viable alternative to the mixed finite element methods and nonconforming (plate) finite element methods for solving fourth order partial differential equations.

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