Published

Convergence Analysis of V-Cycle Multigrid Methods for Anisotropic Elliptic Equations

Yongke Wu, Long Chen, Xiaoping Xie, and Jinchao Xu

IMA Journal on Numerical Analysis. First published online: January 10, 2012.

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ABSTRACT:

 
Fast multigrid solvers for the linear systems arising from the
bilinear finite element discretizations of second order elliptic
equations with anisotropic diffusion are considered. The nearly
optimal convergence of V-cycle multigrid methods, in both the
semi-coarsening and uniform coarsening cases, is established using XZ
identity. Since the ``regularity assumption" is not used in our
analysis, our results can be extended to general domains consisting of
rectangles.