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 | References | Similar Articles | Additional Information

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.