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

2023/03/17 by Cesmelioglu, A., Lee, J. J., Rhebergen, S. · 2 citations
#65M12 #65M15 #65M60 #76D05 #76S99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2303.09882

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.

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