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A family of mixed finite elements for the elasticity problem. (English) Zbl 0632.73063
A new mixed finite element formulation for the equations of linear elasticity is considered. In the formulation the variables approximated are the displacement, the unsymmetric stress tensor and the rotation. The rotation act as a Lagrange multiplier introduced in order to enforce the symmetry of the stress tensor. Based on this formulation a new family of both two- and three-dimensional mixed methods is defined. Optimal error estimates, which are valid uniformly with respect to the Poisson ratio, are derived. Finally, a new postprocessing scheme for improving the displacement is introduced and analyzed.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
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