## Acceleration of a two-grid method for eigenvalue problems

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- by Xiaozhe Hu and Xiaoliang Cheng PDF
- Math. Comp.
**80**(2011), 1287-1301 Request permission

## Abstract:

This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a slightly different linear problem on the fine grid, the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Numerical examples are also provided to demonstrate the efficiency of the new method.## References

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## Additional Information

**Xiaozhe Hu**- Affiliation: Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People’s Republic of China
- MR Author ID: 793307
- Email: huxiaozhezju@gmail.com
**Xiaoliang Cheng**- Affiliation: Department of Mathematics, Zhejiang University, Yuquan Campus, Hangzhou, 310027, People’s Republic of China
- Email: xiaoliangcheng@zju.edu.cn
- Received by editor(s): October 21, 2009
- Received by editor(s) in revised form: June 15, 2010
- Published electronically: February 18, 2011
- Additional Notes: This work was supported in part by National Science Foundation of China (No. 10871179).
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**80**(2011), 1287-1301 - MSC (2010): Primary 65L15, 65N15, 65N25, 65N30, 65N55
- DOI: https://doi.org/10.1090/S0025-5718-2011-02458-0
- MathSciNet review: 2785459