On the construction of optimal mixed finite element methods for the linear elasticity problem (Q1057634)

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.