An analysis of HDG methods for the vorticity-velocity-pressure formulation of the stokes problem in three dimensions

We provide the first a priori error analysis of a hybridizable discontinuous Galerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equations of incompressible fluid flow. By using a projection-based approach, we prove that, when all the unknowns use polynomials of degree k ≥ 0, the L2-norm of the errors in the approximate vorticity and pressure converge to zero with order k+1/2, whereas the error in the approximate velocity converges with order k + 1.