An analysis of HDG methods for the vorticity-velocity-pressure formulation of the Stokes problem in three dimensions (Q2894511)

The paper presents a discontinuous Galerkin method for the steady Stokes equation in three space dimensions. The vorticity-velocity-pressure formulation is discretized in a Lipschitz polyhedron. Hybridization is used to generate divergence-free approximate velocity fields. An a priori error analysis is presented. A projection-based approach is to prove that the approximated vorticity and pressure, which are polynomials of degree \(k\), converge with order \(k+{1\over 2}\) in the \(L_2\)-norm for any \(k\geq0\). The velocity field is shown to converge with order \(k+1\). Furthermore, the estimates of the projection of the errors are shown to be independent of the stabilization function.