A novel parameter-free and locking-free enriched Galerkin method for linear elasticity

We propose a novel parameter-free and locking-free enriched Galerkin (EG) method for solving the linear elasticity problem in both two and three dimensions. Unlike existing locking-free EG methods, our method enriches the first-order continuous Galerkin (CG) space with piecewise constants along edges in two dimensions or faces in three dimensions. This enrichment acts as a correction to the normal component of the CG space, ensuring the locking-free property and delivering an oscillation-free stress approximation without requiring post-processing. Our theoretical analysis establishes the well-posedness of the method and derives optimal error estimates. Numerical experiments further demonstrate the accuracy, efficiency, and robustness of the proposed method.