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A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity

Author: Susanne C. Brenner
Journal: Math. Comp. 63 (1994), 435-460
MSC: Primary 73V05; Secondary 65M55, 73C99, 73V20
MathSciNet review: 1257574
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Abstract: A robust optimal-order multigrid method for the pure traction problem in two-dimensional linear elasticity is studied. The finite element discretization is a variant of a mixed method proposed by Falk where the displacement is approximated by nonconforming piecewise linear functions and the "pressure" is approximated by piecewise constant functions on a coarser grid. Full multigrid convergence is obtained. The performance of this multigrid algorithm does not deteriorate as the material becomes nearly incompressible.

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Keywords: Linear elasticity, mixed finite element, multigrid, nonconforming, traction problem
Article copyright: © Copyright 1994 American Mathematical Society