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Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition
Authors:Xiaobing Feng  Ohannes A Karakashian
Institution:Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996 ; Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
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.

Keywords:Biharmonic equation  Cahn-Hilliard equation  discontinuous Galerkin methods  dynamic meshes  error estimates
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