Abstract
An optimal order multigrid method is developed for the pure displacement problem in two-dimensional linear elasticity. It is based on a nonconforming mixed formulation, where the displacement is approximated by weakly continuous piecewise linear vector functions, and the pressure is approximated by piecewise constants. The full multigrid convergence is proved. The performance of the multigrid method does not deteriorate as the material becomes nearly incompressible.
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