Nonconforming mixed finite elements for linear elasticity on simplicial grids

This paper introduces a new family of nonconforming mixed finite elements for solving the linear elasticity equations on simplicial grids. Besides, this paper describes the construction of the lowest order basis functions. The construction only involves simple computations due to the new explicit stress shape function spaces and the procedure applies for high order cases. Numerical experiments for four benchmark problems in mechanics indicate the robust locking-free behavior and show that the lowest order nonconforming mixed method leads to smaller stress errors than the first and second order standard Galerkin methods for the nearly incompressible case.