| Issue |
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
|
|
|---|---|---|
| Page(s) | 273 - 302 | |
| DOI | https://doi.org/10.1051/m2an/2023086 | |
| Published online | 16 February 2024 | |
A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem
1
Department of Mathematics and Statistics, Oakland University, MI, USA
2
Department of Mathematics, Baylor University, TX, USA
3
Department of Applied Mathematics, University of Waterloo, ON, Canada
* Corresponding author: srheberg@uwaterloo.ca
Received:
17
March
2023
Accepted:
18
October
2023
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.
Mathematics Subject Classification: 65M12 / 65M15 / 65M60 / 76D05 / 76S99
Key words: Discontinuous Galerkin / hybridized methods / Navier–Stokes equations / Darcy’s equations / Beavers–Joseph–Saffman condition
© The authors. Published by EDP Sciences, SMAI 2024
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