A new continuous/discontinuous formulation for Stokes problem with analysis of InfSup stability

In this paper we present a new continuous/discontinuous finite element method with continuous trace space for Stokes problem. This new method has two new bi-linear forms which are responsible for the properties of the method. One of these two new bi-linear forms allows to eliminate completely the discontinuous pressure at element level preserving the convergence rates. The other bi-linear form allows interpolation of any order for pressure to be possible since the order of interpolation for the velocity and for the trace variable or hybrid variable satisfies a limit well determined. The InfSup stability condition is well established for any order of interpolation of the pressure and for arbitrary meshes. Numerical experiments indicate optimal rates of convergence, and that, for the Stokes problem, the method presented in this paper has computational cost lower than that of the Galerkin method with continuous or discontinuous pressure and of the HDG method with discontinuous trace space, for solving the global system using direct solver. Finally, it must be observed that the formulation and the analysis presented here are naturally extended if we used discontinuous trace space.