A multilevel successive iteration method for nonlinear elliptic problems

Yunqing Huang; Zhongci Si; Tao TANG; Weimin Xue

doi:10.1090/S0025-5718-03-01566-7

A multilevel successive iteration method for nonlinear elliptic problems

Yunqing Huang^*, Zhongci Si, Tao TANG, Weimin Xue

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

35 Citations (Scopus)

Abstract

In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearizartion 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.

Original language	English
Pages (from-to)	525-539
Number of pages	15
Journal	Mathematics of Computation
Volume	73
Issue number	246
DOIs	https://doi.org/10.1090/S0025-5718-03-01566-7
Publication status	Published - Apr 2004

Scopus Subject Areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Cascadic algorithm
Complexity
Error estimate
Finite element method
Multigrid method
Nonlinear elliptic problem

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10.1090/S0025-5718-03-01566-7

Cite this

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title = "A multilevel successive iteration method for nonlinear elliptic problems",

abstract = "In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearizartion 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.",

keywords = "Cascadic algorithm, Complexity, Error estimate, Finite element method, Multigrid method, Nonlinear elliptic problem",

author = "Yunqing Huang and Zhongci Si and Tao TANG and Weimin Xue",

note = "The research of Y. Huang and Z. Shi was supported in part by special funds for Major State Basic Research Projects of China, and Y. Huang was also supported in part by the National Education Ministry. The research of T. Tang and W. Xue was supported by the FRG grants of the Hong Kong Baptist University and the RGC grants of the Hong Kong Research Grants Council. ",

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doi = "10.1090/S0025-5718-03-01566-7",

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TY - JOUR

T1 - A multilevel successive iteration method for nonlinear elliptic problems

AU - Huang, Yunqing

AU - Si, Zhongci

AU - TANG, Tao

AU - Xue, Weimin

N1 - The research of Y. Huang and Z. Shi was supported in part by special funds for Major State Basic Research Projects of China, and Y. Huang was also supported in part by the National Education Ministry. The research of T. Tang and W. Xue was supported by the FRG grants of the Hong Kong Baptist University and the RGC grants of the Hong Kong Research Grants Council.

PY - 2004/4

Y1 - 2004/4

N2 - In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearizartion 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.

AB - In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearizartion 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.

KW - Cascadic algorithm

KW - Complexity

KW - Error estimate

KW - Finite element method

KW - Multigrid method

KW - Nonlinear elliptic problem

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U2 - 10.1090/S0025-5718-03-01566-7

DO - 10.1090/S0025-5718-03-01566-7

M3 - Journal article

AN - SCOPUS:1642618486

SN - 0025-5718

VL - 73

SP - 525

EP - 539

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 246

ER -

A multilevel successive iteration method for nonlinear elliptic problems

Abstract

Scopus Subject Areas

User-Defined Keywords

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