A Robust V-cycle multigrid method is constructed for the linear system arising from the bilinear finite element discretization of anisotropic linear elasticity equations. By using the Xu-Zikatanov (XZ) identity, quasi-optimal convergence of the method is established in the sense that the multigrid method is independent of the parameterε and dependent on h in a very weakly way. Since the 'regularity assumption' is not used in the analysis, the results can be extended to domains consisting of rectangles. Numerical experiments confirm the theoretical results.
