On the construction of optimal mixed finite element methods for the linear elasticity problem. (English) Zbl 0563.65072

We consider the mixed formulation of the finite element method for linear elasticity, i.e. a formulation where independent approximations are used for both the stresses and the displacements. In the first part of the paper the application of the Babuška-Brezzi theory to this problem is discussed and it is shown, that the use of certain mesh-dependent norms simplifies the analysis considerably. The remaining of the paper is devoted to the construction of mixed methods with optimal convergence rates. A systematic way of constructing such methods is proposed and finally the ideas are applied in some examples.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
35J25 Boundary value problems for second-order elliptic equations
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