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A multilevel successive iteration method for nonlinear elliptic problems


Authors: Yunqing Huang, Zhongci Shi, Tao Tang and Weimin Xue
Journal: Math. Comp. 73 (2004), 525-539
MSC (2000): Primary 65F10, 65N30, 65N55
DOI: https://doi.org/10.1090/S0025-5718-03-01566-7
Published electronically: July 14, 2003
MathSciNet review: 2028418
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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.


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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

DOI: https://doi.org/10.1090/S0025-5718-03-01566-7
Keywords: Multigrid method, cascadic algorithm, finite element method, nonlinear elliptic problem, error estimate, complexity
Received by editor(s): June 6, 2000
Received by editor(s) in revised form: October 12, 2002
Published electronically: July 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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