A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem

We present and analyze a strongly conservative hybridizable discontinuous Galerkin finite element method for the coupled incompressible Navier-Stokes and Darcy problem with Beavers-Joseph-Saffman interface condition. An a priori error analysis shows that the velocity error does not depend on the pressure, and that velocity and pressure converge with optimal rates. These results are confirmed by numerical examples.