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In this paper, we develop an arbitrary-order locking-free enriched Galerkinmethod for the linear elasticity problem using the stress-displacementformulation in both two and three dimensions. The method is based on the mixeddiscontinuous Galerkin method in [30], but with a different stressapproximation space that enriches the arbitrary order continuous Galerkin spacewith some piecewise symmetric-matrix valued polynomials. We prove that themethod is well-posed and provide a parameter-robust error estimate, whichconfirms the locking-free property of the EG method. We present some numericalexamples in two and three dimensions to demonstrate the effectiveness of theproposed method.

A locking-free mixed enriched Galerkin method of arbitrary order for linear elasticity using the stress-displacement formulation