A multilevel successive iteration method for nonlinear elliptic problems

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 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 languageEnglish
Pages (from-to)525-539
Number of pages15
JournalMathematics of Computation
Volume73
Issue number246
DOIs
Publication statusPublished - 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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