Analysis of the Staggered DG Method for the Quasi-Newtonian Stokes flows

This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and eliminates the pressure variable via the incompressibility condition. Thanks to the subtle construction of the finite element spaces used in our staggered DG method, no additional numerical flux or stabilization terms are needed. Based on the abstract theory for the non-linear twofold saddle point problems, we prove the well-posedness of our scheme. A priori error analysis for all the involved unknowns is also provided. In addition, the proposed scheme can be hybridizable and the global problem only involves the trace variables, rendering the method computationally attractive. Finally, several numerical experiments are carried out to illustrate the performance of our scheme.