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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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Additional Information
  • Xiaobing Feng
  • Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
  • MR Author ID: 351561
  • Email: xfeng@math.utk.edu
  • Ohannes A. Karakashian
  • Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37996
  • Email: ohannes@math.utk.edu
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 1093-1117
  • MSC (2000): Primary 65M15, 65M60, 74N20
  • DOI: https://doi.org/10.1090/S0025-5718-07-01985-0
  • MathSciNet review: 2299767