A multilevel successive iteration method for nonlinear elliptic problems

Huang, Yunqing; Shi, Zhongci; Tang, Tao; Xue, Weimin

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

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.

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