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Volume 17, Issue 1
An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation

Jie Zhou, Long Chen, Yunqing Huang & Wansheng Wang

DOI: 10.4208/cicp.231213.100714a

Commun. Comput. Phys., 17 (2015), pp. 127-145.

Published online: 2018-04

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  • Abstract

A two-grid method for solving the Cahn-Hilliard equation is proposed in this paper. This two-grid method consists of two steps. First, solve the Cahn-Hilliard equation with an implicit mixed finite element method on a coarse grid. Second, solve two Poisson equations using multigrid methods on a fine grid. This two-grid method can also be combined with local mesh refinement to further improve the efficiency. Numerical results including two and three dimensional cases with linear or quadratic elements show that this two-grid method can speed up the existing mixed finite method while keeping the same convergence rate.

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@Article{CiCP-17-127, author = {Jie Zhou, Long Chen, Yunqing Huang and Wansheng Wang}, title = {An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation}, journal = {Communications in Computational Physics}, year = {2018}, volume = {17}, number = {1}, pages = {127--145}, abstract = {

A two-grid method for solving the Cahn-Hilliard equation is proposed in this paper. This two-grid method consists of two steps. First, solve the Cahn-Hilliard equation with an implicit mixed finite element method on a coarse grid. Second, solve two Poisson equations using multigrid methods on a fine grid. This two-grid method can also be combined with local mesh refinement to further improve the efficiency. Numerical results including two and three dimensional cases with linear or quadratic elements show that this two-grid method can speed up the existing mixed finite method while keeping the same convergence rate.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.231213.100714a}, url = {http://global-sci.org/intro/article_detail/cicp/10953.html} }
TY - JOUR T1 - An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation AU - Jie Zhou, Long Chen, Yunqing Huang & Wansheng Wang JO - Communications in Computational Physics VL - 1 SP - 127 EP - 145 PY - 2018 DA - 2018/04 SN - 17 DO - http://doi.org/10.4208/cicp.231213.100714a UR - https://global-sci.org/intro/article_detail/cicp/10953.html KW - AB -

A two-grid method for solving the Cahn-Hilliard equation is proposed in this paper. This two-grid method consists of two steps. First, solve the Cahn-Hilliard equation with an implicit mixed finite element method on a coarse grid. Second, solve two Poisson equations using multigrid methods on a fine grid. This two-grid method can also be combined with local mesh refinement to further improve the efficiency. Numerical results including two and three dimensional cases with linear or quadratic elements show that this two-grid method can speed up the existing mixed finite method while keeping the same convergence rate.

Jie Zhou, Long Chen, Yunqing Huang and Wansheng Wang. (2018). An Efficient Two-Grid Scheme for the Cahn-Hilliard Equation. Communications in Computational Physics. 17 (1). 127-145. doi:10.4208/cicp.231213.100714a
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