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A discontinuous Galerkin finite element method for the Cahn-Hilliard equation
Liu Lijie 1, Gong Yurong 2
1. College of Science, Henan University of Technology, Zhengzhou, Henan 450001, P.R. China
2. Zhengzhou Chenggong University of Finance and Economics, Gongyi, Henan 451200, P.R. China
*Correspondence author
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Funding: none
Opened online:26 February 2016
Accepted by: none
Citation: Liu Lijie, Gong Yurong.A discontinuous Galerkin finite element method for the Cahn-Hilliard equation[OL]. [26 February 2016] http://en.paper.edu.cn/en_releasepaper/content/4678069
 
 
In this paper, we develop, analysis and testthe Discontinuous Galerkin (DG) finite element method for the fourth orderCahn-Hilliard equation in one dimension. The method, which isdifferent from the traditional local discontinuous Galerkin (LDG)method, can be applied without introducing any auxiliary variablesor rewriting the original equation into a larger system. we provestability by choosing interface numerical fluxes carefully, finallyfor the linear case, a $O(h^{k-1})$ error estimate can be proved forpiecewise polynomials of degree $k$ when $kgeq 3$.
Keywords: Cahn-Hilliard equation, Discontinuous Galerkinmethod, Stability, Error Estimates.
 
 
 

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