STAGGERED DG METHODS FOR THE PSEUDOSTRESS-VELOCITY FORMULATION OF THE STOKES EQUATIONS ON GENERAL MESHES

In this paper, we introduce staggered discontinuous Galerkin methods for the stationary Stokes flow on polygonal meshes. The proposed method is based on the pseudostress-velocity formulation. A Lagrange multiplier on dual edges is introduced to impose the continuity of the pseudostress, which reduces the size of the final system via hybridization and eases the construction of the finite element space for the approximation of the pseudostress. The resulting method is stable and optimally convergent even on distorted or concave polygonal meshes. In addition, hanging nodes can be automatically incorporated in the construction of the method, which favors adaptive mesh refinement. Two types of local postprocessing for the velocity field are proposed to obtain one order higher convergence. Numerical experiments are provided to validate the theoretical findings and demonstrate the performance of the proposed method.