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Finite Elements and Fast Iterative Solverswith Applications in Incompressible Fluid Dynamics$
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Howard Elman, David Silvester, and Andy Wathen

Print publication date: 2014

Print ISBN-13: 9780199678792

Published to Oxford Scholarship Online: September 2014

DOI: 10.1093/acprof:oso/9780199678792.001.0001

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The Navier–Stokes Equations

The Navier–Stokes Equations

Chapter:
(p.333) 8 The Navier–Stokes Equations
Source:
Finite Elements and Fast Iterative Solvers
Author(s):

Howard C. Elman

David J. Silvester

Andrew J. Wathen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199678792.003.0009

This chapter concerns the statement and properties of the steady Navier–Stokes equations and the corresponding weak formulation. This includes discussion of stability theory, bifurcation and nonlinear iteration. This is followed by a description of finite element discretization and error analysis of discrete solutions.

Keywords:   Navier–Stokes, stability, bifurcation, finite elements, error analysis

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