A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field

We introduce a hybridizable discontinuous Galerkin method for the incompressible Navier–Stokes equations for which the approximate velocity field is pointwise divergence-free. The method proposed here builds on the method presented by Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889–A913]. We show that with simple modifications of the function spaces in the method of Labeur and Wells that it is possible to formulate a simple method with pointwise divergence-free velocity fields, and which is both momentum conserving and energy stable. Theoretical results are verified by twoand three-dimensional numerical examples and for different orders of polynomial approximation.