On the equivalence of mode decomposition and mixed finite elements based on the hellinger-reissner principle. part I: Theory

A theorem is presented which defines the conditions under which an equivalent mixed finite element based on the Hellinger-Reissner principle exists for a given mode decomposition element. Mode decomposition elements are a family of elements in which parasitic stresses are removed by a suitable projection to enhance the rate of convergence of elements which tend to lock; so far they were outside of any standard finite element formulation. Elements that, by virtue of this theorem, are found equivalent to appropriate mixed elements can be then analyzed by techniques which exist within the framework of Hellinger-Reissner formalism.