Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open. 1991 Mathematics Subject Classification: Primary 73C35; Secondary 73C50, 58F05, 58A17. Research of the first author partially supported by the grant of the University of Lodź no. 505/454. The paper is in final form and no version of it will be published elsewhere.