Convergence analysis of V-Cycle multigrid methods for anisotropic elliptic equations

Yongke Wu, Long Chen, Xiaoping Xie, Jinchao Xu

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Fast multigrid solvers are considered for the linear systems arising from the bilinear finite element discretizations of second-order elliptic equations with anisotropic diffusion. Optimal convergence of Vcycle multigrid methods in the semicoarsening case and nearly optimal convergence of V-cycle multigrid method with line smoothing in the uniformly-coarsening case are established using the Xu-Zikatanov identity. Since the 'regularity assumption' is not used in the analysis, the results can be extended to general domains consisting of rectangles.

Original languageEnglish (US)
Pages (from-to)1329-1347
Number of pages19
JournalIMA Journal of Numerical Analysis
Volume32
Issue number4
DOIs
StatePublished - Oct 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

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