The families of nonconforming mixed finite elements for linear elasticity on simplex grids

Abstract

We present a new family of nonconforming tetrahedral elements and a new family of nonconforming triangular elements for the stress-displacement system of linear elasticity problem. The local degrees of freedom of stress field only contain the normal moments on faces (sides) of element and the moments on element. The shape function spaces are simple, local, explicitly represented, and affine-equivalent. We also present two families simplified lowest-order finite elements by using the rigid motion model, and demonstrate our theory numerically in 2D area.