2023/04/29 by Zhongshu Zhao, Zhao, Zhongshu, Hui Peng +5 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2305.00150
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.