Nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity
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.
Publication Source (Journal or Book title)
SIAM Journal on Numerical Analysis
Brenner, S. (1993). Nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity. SIAM Journal on Numerical Analysis, 30 (1), 116-135. https://doi.org/10.1137/0730006