Discontinuous Galerkin Methods With Interior Penalty For Linear Elasticity

In this paper,a family of discontinuous Galerkin methods with interior penalty are studied to solve the linear elasticity problem.We provide a unified basic framework for these methods and analyze their priori error estimates.The posedness of these schemes,the optimal convergence rates in energy norm for all the schemes,and the optimal conver-gence rates in L2 norm for symmetric schemes are proved.Due to adjoint inconsistency,the convergence rates of L2 norm error is not optimal generally for nonsymmetric schemes.Therefore,superpenalty is introduced to overcome the error caused by the adjoint incon-sistency so that the optimal convergence rate in L2 norm is achieved.Further,we establish an explicit posteriori error estimate based on L2 norm and prove its effectiveness.Nu-merical results are given to confirm the correctness of theoretical analysis.