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A two-grid discretization method for decoupling systems of partial differential equations


Authors: Jicheng Jin, Shi Shu and Jinchao Xu
Journal: Math. Comp. 75 (2006), 1617-1626
MSC (2000): Primary 65N50, 65N30
DOI: https://doi.org/10.1090/S0025-5718-06-01869-2
Published electronically: July 11, 2006
MathSciNet review: 2240627
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Abstract: In this paper, we propose a two-grid finite element method for solving coupled partial differential equations, e.g., the Schrödinger-type equation. With this method, the solution of the coupled equations on a fine grid is reduced to the solution of coupled equations on a much coarser grid together with the solution of decoupled equations on the fine grid. It is shown, both theoretically and numerically, that the resulting solution still achieves asymptotically optimal accuracy.


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Additional Information

Jicheng Jin
Affiliation: Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People’s Republic of China
Email: jjc@xtu.edu.cn

Shi Shu
Affiliation: Institute for Computational and Applied Mathematics and Department of Mathematics, Xiangtan University, People’s Republic of China
Email: shushi@xtu.edu.cn

Jinchao Xu
Affiliation: Institute for Computational and Applied Mathematics, Xiangtan University, People’s Republic of China; and Center for Computational Mathematics and Applications, Pennsylvania State University, Pennsylvania
Email: xu@math.psu.edu

DOI: https://doi.org/10.1090/S0025-5718-06-01869-2
Keywords: Schr\"{o}dinger type equation, coupled system, finite element method, two-grid.
Received by editor(s): May 19, 2005
Received by editor(s) in revised form: August 15, 2005
Published electronically: July 11, 2006
Additional Notes: The research of the first and second authors was supported by NSAF(10376031) and the National Major Key Project for Basic Research and National High-Tech ICF Committee in China.
The research of the third author was supported in part by NSF DMS-0209497 and NSF DMS-0215392 and the Furong Scholar Program of Hunan Province through Xiangtan University
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.