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We present a superconvergent hybridizable discontinuous Galerkin (HDG) methodfor the steady-state incompressible Navier-Stokes equations on generalpolyhedral meshes. For arbitrary conforming polyhedral mesh, we use polynomialsof degree k+1, k, k to approximate the velocity, velocity gradient andpressure, respectively. In contrast, we only use polynomials of degree k toapproximate the numerical trace of the velocity on the interfaces. Since thenumerical trace of the velocity field is the only globally coupled unknown,this scheme allows a very efficient implementation of the method. For thestationary case, and under the usual smallness condition for the source term,we prove that the method is well defined and that the global L2-norm of theerror in each of the above-mentioned variables and the discrete H1-norm of theerror in the velocity converge with the order of k+1 for k>=0. We also showthat for k>=1, the global L2-norm of the error in velocity converges with theorder of k+2. From the point of view of degrees of freedom of the globallycoupled unknown: numerical trace, this method achieves optimal convergence forall the above-mentioned variables in L2-norm for k>=0, superconvergence for thevelocity in the discrete H1-norm without postprocessing for k>=0, andsuperconvergence for the velocity in L2-norm without postprocessing for k>=1.

A superconvergent HDG method for the Incompressible Navier-Stokes Equations on general polyhedral meshes