A Staggered Discontinuous Galerkin Method for linear elasticity problem on Polytopal Meshes
For computational mechanics researchers, this provides a new method for linear elasticity on complex meshes with theoretical guarantees, though it is an incremental extension of existing DG techniques.
This paper develops a novel staggered discontinuous Galerkin method for linear elasticity on arbitrary polytopal meshes, achieving locking-free behavior and local momentum balance. Numerical experiments validate the theoretical stability and error estimates.
This paper develops a novel staggered discontinuous Galerkin (SDG) method for linear elasticity based on the Hellinger-Reissner variational principle. We construct symmetric stress spaces with normal continuity across element boundaries on arbitrary polytopal meshes, while approximating the displacement field using piecewise polynomial functions defined on the same meshes. The method is locking-free and satisfies a local balance of linear momentum and angular momentum. We present a comprehensive theoretical analysis, including proofs of stability and error estimates. The formulation admits a hybridizable structure, which significantly simplifies the numerical implementation. Numerical experiments validate the theoretical results and demonstrate the effectiveness of the proposed approach.