Multigrid methods for the pure traction problem of linear elasticity: Mixed formulation

Abstract

A multigrid method using conforming P-1 finite elements is developed for the two-dimensional pure traction boundary value problem of linear elasticity. The convergence is uniform even as the material becomes nearly incompressible. A heuristic argument for acceleration of the multigrid method is discussed as well. Numerical results with and without this acceleration as well as performance estimates on a parallel computer are included.