The commonly used linear / constant element cannot be applied in solving elasticity problem because it dissatisfy the LBB condition. In this paper, we derive a stabilization scheme for elasticity problem based on Bochev-Dohrmann-Gunzburger method. We add a consistent term and projection-type stabilization term, which can effectively bypass the inf-sup condition. The advantages of our method are: they do not depend on the space dimension, do not require calculation of higher order derivatives or edge-based data structures.
