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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

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Volume 25, Issue 4


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

Philipp W. Schroeder
  • Corresponding author
  • Institute for Numerical and Applied Mathematics, Georg-August-University Göttingen, D-37083 Göttingen, Germany
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/ Gert Lube
Published Online: 2018-02-22 | DOI: https://doi.org/10.1515/jnma-2016-1101


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.

Keywords: Incompressible viscous flow; divergence-free FEM; pressure/semi-robust error estimates; vortex dynamics

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


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About the article

Received: 2016-10-12

Revised: 2017-01-26

Accepted: 2017-01-29

Published Online: 2018-02-22

Published in Print: 2017-12-20

Citation Information: Journal of Numerical Mathematics, Volume 25, Issue 4, Pages 249–276, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnma-2016-1101.

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