A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

This paper proposes and analyzes a stabilized embedded discontinuous Galerkin (EDG) method for linear elasticity problems. A stabilized term is added in the scheme to ensure locking-free approximations. With a special designed interpolation, we prove the Stokes stable elements in space [H01(Ω)]d×L02(Ω) are also stable in [HD1(Ω)]d×L2(Ω) on general simplicial mesh, and therefore, we prove the underlying EDG method is robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ. Numerical experiments are provided to verify the theoretical results.