Divergence-Free HDG Methods for the Vorticity-Velocity Formulation of the Stokes Problem

We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomials of degree k ≥ 0, the L norm of the errors in the approximate vorticity and pressure converge with order k + 1/2 and the error in the approximate velocity converges with order k + 1. We achieve this by letting the normal stabilization function go to infinity in the error estimates previously obtained for a hybridizable discontinuous Galerkin method.