On spurious oscillations due to irrotational forces in the Navier-Stokes momentum balance

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Date
2015
Volume
2132
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

This contribution studies the in uence of the pressure on the velocity error in finite element discretisations of the Navier-Stokes equations. Three simple benchmark problems that are all close to real-world applications convey that the pressure can be comparably large and is not to be underestimated. For widely used finite element methods like the Taylor-Hood finite element method, such relatively large pressures can lead to spurious oscillations and arbitrarily large errors in the velocity, even if the exact velocity is in the ansatz space. Only mixed finite element methods, whose velocity error is pressure-independent, like the Scott-Vogelius finite element method can avoid this influence.

Description
Keywords
incompressible Navier–Stokes equations, mixed finite element methods, benchmarks, spurious velocity oscillations
Citation
Linke, A., & Merdon, C. (2015). On spurious oscillations due to irrotational forces in the Navier-Stokes momentum balance (Vol. 2132). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
License
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