A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier--Stokes and Darcy problem

Abstract

We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimal a priori error analysis for the fully discrete problem when using Backward Euler time stepping. The theoretical results are verified by numerical examples.