Conforming Rectangular Mixed Finite Elements for Elasticity

We present a new family of rectangular mixed finite elements for the stress-displacement system of the plane elasticity problem. Based on the theory of mixed finite element methods, we prove that they are stable and obtain error estimates for both the stress field and the displacement field. Using the finite element spaces in this family, an exact sequence is established as a discrete version of the elasticity complex in two dimensions. And the relationship between this discrete version and the original one is shown in a commuting diagram.