Title: A hybridizable discontinuous Galerkin method for the Navier--Stokes equations with pointwise divergence-free velocity field,
Abstract: 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 builds on the method presented
by Labeur and Wells [SIAM J. Sci. Comput., vol. 34 (2012), pp. A889--A913]. We
show that with modifications of the function spaces in the method of Labeur and
Wells it is possible to formulate a simple method with pointwise
divergence-free velocity fields which is momentum conserving, energy stable,
and pressure-robust. Theoretical results are supported by two- and
three-dimensional numerical examples and for different orders of polynomial
approximation.