  We propose two classes of mixed finite elements for linear elasticity of any
order, with interior penalty for nonconforming symmetric stress approximation.
One key point of our method is to introduce some appropriate nonconforming
face-bubble spaces based on the local decomposition of discrete symmetric
tensors, with which the stability can be easily established. We prove the
optimal error estimate for both displacement and stress by adding an interior
penalty term. The elements are easy to be implemented thanks to the explicit
formulations of its basis functions. Moreover, the methods can be applied to
arbitrary simplicial grids for any spatial dimension in a unified fashion.
Numerical tests for both 2D and 3D are provided to validate our theoretical
results.
