A multilevel successive iteration method for nonlinear elliptic problems
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- by Yunqing Huang, Zhongci Shi, Tao Tang and Weimin Xue PDF
- Math. Comp. 73 (2004), 525-539 Request permission
Abstract:
In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearization technique and the cascadic multigrid approach. The error analysis and the complexity analysis for the proposed method are carried out based on the two-grid theory and its multilevel extension. A superconvergence result for the multilevel linearization algorithm is established, which, besides being interesting for its own sake, enables us to obtain the error estimates for the multilevel successive iteration method. The optimal complexity is established for nonlinear elliptic problems in 2-D provided that the number of grid levels is fixed.References
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Additional Information
- Yunqing Huang
- Affiliation: Department of Mathematics and Institute for Computational and Applied Mathematics, Xiangtan University, Xiangtan, Hunan 411105, Peoples Republic of China
- Email: huangyq@xtu.edu.cn
- Zhongci Shi
- Affiliation: Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, 100080, Peoples Republic of China
- Email: shi@lsec.cc.ac.cn
- Tao Tang
- Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Email: ttang@math.hkbu.edu.hk
- Weimin Xue
- Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Email: wmxue@math.hkbu.edu.hk
- Received by editor(s): June 6, 2000
- Received by editor(s) in revised form: October 12, 2002
- Published electronically: July 14, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 525-539
- MSC (2000): Primary 65F10, 65N30, 65N55
- DOI: https://doi.org/10.1090/S0025-5718-03-01566-7
- MathSciNet review: 2028418