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Volume 5, Issue 2-4
Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hilliard System

Yinhua Xia, Yan Xu & Chi-Wang Shu

Commun. Comput. Phys., 5 (2009), pp. 821-835.

Published online: 2009-02

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  • Abstract

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for the nonlinear problems which include the Allen-Cahn/Cahn-Hilliard system for one-dimensional and two-dimensional cases demonstrate the accuracy and capability of the numerical method. 

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@Article{CiCP-5-821, author = {Yinhua Xia, Yan Xu and Chi-Wang Shu}, title = {Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hilliard System}, journal = {Communications in Computational Physics}, year = {2009}, volume = {5}, number = {2-4}, pages = {821--835}, abstract = {

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for the nonlinear problems which include the Allen-Cahn/Cahn-Hilliard system for one-dimensional and two-dimensional cases demonstrate the accuracy and capability of the numerical method. 

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7765.html} }
TY - JOUR T1 - Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hilliard System AU - Yinhua Xia, Yan Xu & Chi-Wang Shu JO - Communications in Computational Physics VL - 2-4 SP - 821 EP - 835 PY - 2009 DA - 2009/02 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7765.html KW - AB -

In this paper, we consider the application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system. The method in this paper extends the local discontinuous Galerkin method in [10] to the more general application system which is coupled with the Allen-Cahn and Cahn-Hilliard equations. Similar energy stability result as that in [10] is presented. Numerical results for the nonlinear problems which include the Allen-Cahn/Cahn-Hilliard system for one-dimensional and two-dimensional cases demonstrate the accuracy and capability of the numerical method. 

Yinhua Xia, Yan Xu and Chi-Wang Shu. (2009). Application of the Local Discontinuous Galerkin Method for the Allen-Cahn/Cahn-Hilliard System. Communications in Computational Physics. 5 (2-4). 821-835. doi:
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