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Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier–Stokes flows

Philipp W. Schroeder and Gert Lube

Abstract

This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier–Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the velocity that hold independently of both pressure and Reynolds number. Here, a key aspect is the use of the discrete Stokes projection for the error splitting. Optionally, edge-stabilisation can be included in the case of dominant convection. Emphasising the importance of conservation properties, the theoretical results are complemented with numerical simulations of vortex dynamics and laminar boundary layer flows.

MSC 2010: 65M12; 65M15; 65M60; 76D05; 76D10; 76D17

Acknowledgements

We gratefully acknowledge the comments and suggestions on this manuscript from the anonymous reviewers.

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Received: 2016-10-12
Revised: 2017-1-26
Accepted: 2017-1-29
Published Online: 2018-2-22
Published in Print: 2017-12-20

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