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A nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity. (English) Zbl 0767.73068

Summary: 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
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