Richard Falk
Department of Mathematics
Rutgers University

Abstract. One successful approach to constructing stable finite element methods for the equations of linear elasticity that produce direct approximations to both stresses and displacements is to base them on a modified form of the Hellinger--Reissner variational principle that only weakly imposes the symmetry condition on the stresses. In this talk, we explore the derivation and analysis of such methods.

One key idea is to use the close connection between finite element differential complexes and the stability of finite element methods. By exploiting a connection between a differential complex related to the equations of elasticity and the de Rham complex, we show how a new simple class of stable finite element approximations for the equations of elasticity can be developed, and how many previously developed methods can be fit in a common structure.