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

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 er...

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Bibliographic Details
Published in:Mathematics of computation 2007-07, Vol.76 (259), p.1093-1117
Main Authors: Feng, Xiaobing, Karakashian, Ohannes A.
Format: Article
Language:English
Subjects:
A priori knowledge
Approximation
Calculus of variations and optimal control
Error rates
Estimation methods
Exact sciences and technology
Finite element method
Galerkin methods
Interpolation
Mathematical analysis
Mathematical discontinuity
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Polynomials
Research article
Sciences and techniques of general use
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Summary: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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-07-01985-0