Analysis of a reduced-order HDG method for the Stokes equations

In this paper, we analyze a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Stokes equations. The reduced stabilization enables us to reduce the number of facet unknowns and improve the computational efficiency of the method. We provide optimal error estimates in an energy and $L^2$ norms. It is shown that the reduced method with the lowest-order approximation is closely related to the nonconforming Crouzeix-Raviart finite element method. We also prove that the solution of the reduced method converges to the nonconforming Gauss-Legendre finite element solution as a stabilization parameter $τ$ tends to infinity and that the convergence rate is $O(τ^{-1})$.