Multigrid method for the equilibrium equations of elasticity using a compact scheme (Q1091855)

A compact difference scheme derived by \textit{T. N. Phillips} and \textit{M. E. Rose}, SIAM J. Stat. Comput. 7, 288-301 (1986) for treating the equilibrium equations of elasticity is studied. The scheme turns out to be inconsistent and unstable. A multigrid method which takes into account these properties is described. The solution of the discrete equations, up to the level of discretization errors, is obtained by this method in just 16 work units, where a work unit is the work involved in relaxing the finest grid equations once.