A staggered cell-centered finite element method for Stokes problems with variable viscosity on general meshes

In this paper, we propose to extend the staggered cell-centered finite element method (SCFEM) on general meshes for the Stokes problems with variable viscosity (possibly discontinuous). The scheme is cell-centered in the sense that the solution can be computed by cell unknowns of the primal mesh and the dual mesh for the velocity and the pressure, respectively, where the velocity is approximated by piecewise linear functions (P-1) on the triangular dual submesh, and the pressure is approximated by piece wise constant functions (P-0) on the dual mesh. In order to get the local continuity of numerical stresses across the interfaces, the scheme gives the auxiliary edge unknowns interpolated by the multipoint stress approximation technique. Its stability and convergence properties are presented in the rigorous theoretical framework. Numerical results are carried out to highlight accuracy and computational cost.