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Published in:
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2016 | OriginalPaper | Chapter

1. Introduction

Author : Volker John

Published in: Finite Element Methods for Incompressible Flow Problems

Publisher: Springer International Publishing

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Abstract

The behavior of incompressible fluids is modeled with the system of the incompressible Navier–Stokes equations. These equations describe the conservation of linear momentum and the conservation of mass. In the special case of a steady-state situation and large viscosity of the fluid, the Navier–Stokes equations can be approximated by the Stokes equations. Incompressible flow problems are not only of interest by themselves, but they are part of many complex models for describing phenomena in nature or processes in engineering and industry.

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next chapter The Navier–Stokes Equations as Model for Incompressible Flows
Literature
Boffi D, Brezzi F, Fortin M (2008) Finite elements for the Stokes problem. In: Boffi D, Gastaldi L (eds) Mixed finite elements, compatibility conditions, and applications. Lecture notes in mathematics, vol 1939. Lectures given at the C.I.M.E. Summer School held in Cetraro, June 26–July 1, 2006. Springer, Berlin, pp 45–100
Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Rev Française Automat Informat Recherche Opérationnelle Sér. Rouge 8:129–151MathSciNetMATH
Elman HC, Silvester DJ, Wathen AJ (2014) Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Numerical mathematics and scientific computation, 2nd edn. Oxford University Press, Oxford, pp xiv+479
Girault V, Raviart P-A (1979) Finite element approximation of the Navier-Stokes equations. Lecture notes in mathematics, vol 749. Springer, Berlin/New York, pp vii+200
Girault V, Raviart P-A (1986) Finite element methods for Navier-Stokes equations. Theory and algorithms. Springer series in computational mathematics, vol 5. Springer, Berlin, pp x+374
Layton W (2008) Introduction to the numerical analysis of incompressible viscous flows. Computational science & engineering, vol 6. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, pp xx+213. With a foreword by Max Gunzburger
Metadata
Title
Introduction
Author
Volker John
Copyright Year
2016
Book
Finite Element Methods for Incompressible Flow Problems

Print ISBN: 978-3-319-45749-9

Electronic ISBN: 978-3-319-45750-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-45750-5_1

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