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2020 | OriginalPaper | Chapter

6. Finite Element Pressure Stabilizations for Incompressible Flow Problems

Authors : Volker John, Petr Knobloch, Ulrich Wilbrandt

Published in: Fluids Under Pressure

Publisher: Springer International Publishing

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Abstract

The simulation of incompressible flow problems with pairs of velocity-pressure finite element spaces that do not satisfy the discrete inf-sup condition requires a so-called pressure stabilization. This chapter provides a survey of available methods which are presented for the Stokes problem to concentrate on the main ideas and to avoid additional difficulties originating from more complicated models. The methods can be divided into residual-based stabilizations and stabilizations that utilize only the pressure. For the first class, a comprehensive numerical analysis is presented, whereas for the second class, the presentation is more concise except for a detailed analysis of a local projection stabilization method. Connections of various pressure stabilizations to inf-sup stable discretizations with velocity spaces enriched by bubble functions are also discussed. Numerical studies compare several of the available pressure stabilizations.

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previous chapter Flows of Fluids with Pressure Dependent Material Coefficients

next chapter Finite-Volume Methods for Navier-Stokes Equations

Reading [66], one is wondering that there is no reference to [34] for method (6.107). From the article’s history, one finds that [66] was submitted shortly after [34] was published.

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Title: Finite Element Pressure Stabilizations for Incompressible Flow Problems
Authors: Volker John
Petr Knobloch
Ulrich Wilbrandt
Publisher: Springer International Publishing
Book: Fluids Under Pressure
Print ISBN: 978-3-030-39638-1

Electronic ISBN: 978-3-030-39639-8

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-39639-8_6

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