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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.