A STAGGERED CELL-CENTERED DG METHOD FOR LINEAR ELASTICITY ON POLYGONAL MESHES

We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted. There are three unknowns involved in our formulation: stress, displacement, and rotation. The continuities of the three unknowns are staggered on the interelement boundaries. In addition, the symmetry of the stress tensor is imposed weakly by the introduction of Lagrange multipliers. Optimal a priori error estimates covering low regularities in L² errors of stress, displacement, and rotation are given; in addition, the locking-free error estimates are also investigated. Numerical experiments confirm the theoretical findings and verify the flexibility to rough grids and the locking-free property of the proposed method.