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


Authors: Xiaobing Feng and Ohannes A. Karakashian
Journal: Math. Comp. 76 (2007), 1093-1117
MSC (2000): Primary 65M15, 65M60, 74N20
DOI: https://doi.org/10.1090/S0025-5718-07-01985-0
Published electronically: March 9, 2007
MathSciNet review: 2299767
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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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Additional Information

Xiaobing Feng
Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
Email: xfeng@math.utk.edu

Ohannes A. Karakashian
Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
Email: ohannes@math.utk.edu

DOI: https://doi.org/10.1090/S0025-5718-07-01985-0
Keywords: Biharmonic equation, Cahn-Hilliard equation, discontinuous Galerkin methods, dynamic meshes, error estimates
Received by editor(s): February 1, 2006
Received by editor(s) in revised form: August 31, 2006
Published electronically: March 9, 2007
Additional Notes: The work of the first author was partially supported by the NSF grant DMS-0410266
The work of the second author was partially supported by the NSF grant DMS-0411448
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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