The Staggered DG Method is the Limit of a Hybridizable DG Method. Part II: The Stokes Flow

Abstract

We show that the staggered discontinuous Galerkin (SDG) method (Kim et al. in SIAM J Numer Anal 51:3327---3350, 2013) for the Stokes system of incompressible fluid flow can be obtained from a new hybridizable discontinuous Galerkin (HDG) method by setting its stabilization function to zero at some suitably chosen element faces and by letting it go to infinity at all the remaining others. We then show that, as a consequence, the SDG method immediately acquires three new properties all inherited from this limiting HDG method, namely, its efficient implementation (by hybridization), its superconvergence properties, and its postprocessing of the velocity. In particular, the postprocessing of the velocity is $$\varvec{H}(\mathrm {div})$$H(div)-conforming, weakly divergence-free and converges with order $$k+2$$k+2 where $$k>0$$k>0 is the polynomial degree of the approximations.