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