A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation. (15th March 2023)

• Record Type: Journal Article
• Authors: Chen, Gang; Xie, Xiaoping; Xu, Youcai; Zhang, Yangwen
• Is Part Of: Computers & mathematics with applications. Volume 134(2023)
• Page Start: 66
• Page End: 86
• Publication Date: 2023-03-15
• Subjects: Elasticity -- Stabilized method -- Embedded discontinuous Galerkin (EDG) -- Numerical analysis -- Locking-free; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.12.017
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper proposes and analyzes a stabilized embedded discontinuous Galerkin (EDG) method for linear elasticity problems. A stabilized term is added in the scheme to ensure locking-free approximations. With a special designed interpolation, we prove the Stokes stable elements in space [ H 0 1 ( Ω ) ] d × L 0 2 ( Ω ) are also stable in [ H D 1 ( Ω ) ] d × L 2 ( Ω ) on general simplicial mesh, and therefore, we prove the underlying EDG method is robust in the sense that the derived a priori error estimates are optimal and uniform with respect to the Lamé constant λ . Numerical experiments are provided to verify the theoretical results.