In this paper, we develop an arbitrary-order locking-free enriched Galerkin method for the linear elasticity problem using the stress-displacement formulation in both two and three dimensions. The method is based on the mixed discontinuous Galerkin method in [30], but with a different stress approximation space that enriches the arbitrary order continuous Galerkin space with some piecewise symmetric-matrix valued polynomials. We prove that the method is well-posed and provide a parameter-robust error estimate, which confirms the locking-free property of the EG method. We present some numerical examples in two and three dimensions to demonstrate the effectiveness of the proposed method.

翻译：本文针对二维和三维线弹性问题，基于应力-位移公式，提出了一种任意阶无锁富集Galerkin方法。该方法来源于文献[30]中的混合间断Galerkin方法，但采用了不同的应力逼近空间，该空间将任意阶连续Galerkin空间与一些分片对称矩阵值多项式进行富集。我们证明了该方法的适定性，并给出了参数鲁棒的误差估计，从而确认了该EG方法的无锁特性。本文还给出了二维和三维数值算例，以验证所提方法的有效性。