Pressure robust SUPG-stabilized finite elements for the unsteady Navier–Stokes equation

Abstract In the present contribution, we propose a novel conforming finite element scheme for the time-dependent Navier–Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a ‘divergence-free’ velocity/pressure couple (such as the Sco...

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Bibliographic Details
Published in:IMA journal of numerical analysis 2024-04, Vol.44 (2), p.710-750
Main Authors: Beirão da Veiga, L, Dassi, F, Vacca, G
Format: Article
Language:English
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Summary:Abstract In the present contribution, we propose a novel conforming finite element scheme for the time-dependent Navier–Stokes equation, which is proven to be both convection quasi-robust and pressure robust. The method is built combining a ‘divergence-free’ velocity/pressure couple (such as the Scott–Vogelius element), a discontinuous Galerkin in time approximation and a suitable streamline upwind Petrov–Galerkin-curl stabilization. A set of numerical tests, in accordance with the theoretical results, is included.
ISSN:0272-4979
1464-3642
DOI:10.1093/imanum/drad021