Conforming Rectangular Mixed Finite Elements For Elasticity

In this paper, a new family of conforming mixed finite elements on rectangu-lar meshes are proposed for the stress-displacement system derived from Hellinger-Reissner variational principle for the linear elasticity problem in two dimensions. Based on the theory of mixed finite element methods with the elasticity complex, we analyze their stability and obtain optimal error estimates for both the stress field and the dis-placement field. A discrete vision of the elasticity complex using our finite element spaces is also established, showing that the elements for the stress field are natural discretization of H(div,Ω, S). Then we present their relationship between this discrete sequence and the original one in a commuting diagram.