Primal stabilized hybrid and DG finite element methods for the linear elasticity problem

Primal stabilized hybrid finite element methods for the linear elasticity problem are proposed consisting of locally discontinuous Galerkin problems in the primal variable coupled to a global problem in the multiplier which is identified with the trace of the displacement field. Numerical analysis, covering both continuous or discontinuous interpolations of the multiplier, shows that the proposed formulation preserves the main properties of the associate DG method such as consistency, stability, boundedness and optimal rates of convergence in the energy norm, and in the norm for adjoint consistent formulations. Convergence studies confirm the optimal rates of convergence predicted by the numerical analysis presented here and a local post-processing technique is proposed to recover stress approximations with improved rates of convergence in norm.