A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions

In this article, we to devise superconvergent hybridizable discontinuous Galerkin methods on unstructured polygonal/polyhedral meshes for the Stokes equations of incompressible fluid flow by using M-decompositions. We do this for two formulations of the equations, namely, for the velocity gradient- velocity-pressure formulation, and for the more difficult strain rate-velocity-pressure formulation. We also show how to locally postprocess the approximate velocity to obtain a globally divergence-free and H(div)-conforming velocity converging faster than the original approximate velocity.