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

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. © 2012 The author 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.