| Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 1461 - 1495 | |
| DOI | https://doi.org/10.1051/m2an/2024045 | |
| Published online | 27 August 2024 | |
A hybridizable discontinuous Galerkin method for the coupled Navier–Stokes/Biot problem
1
Department of Mathematics and Statistics, Oakland University, Rochester, MI, USA
2
Department of Mathematics, Baylor University, Waco, TX, USA
3
Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada
* Corresponding author: srheberg@uwaterloo.ca
Received:
22
August
2023
Accepted:
4
June
2024
In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier–Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and prove a priori error estimates. A numerical example confirms our analysis.
Mathematics Subject Classification: 65M12 / 65M15 / 65M60 / 76D05 / 76S99
Key words: Navier–Stokes equations / Biot’s consolidation model / poroelasticity / Beavers–Joseph–Saffman / hybridized methods / discontinuous Galerkin
© The authors. Published by EDP Sciences, SMAI 2024
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