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Preliminaries, Notation, and Spaces of Functions Read chapter Read first chapter

2016 | OriginalPaper | Chapter

7. Numerical Method

Authors : Eduard Feireisl, Trygve G. Karper, Milan Pokorný

Published in: Mathematical Theory of Compressible Viscous Fluids

Publisher: Springer International Publishing

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Abstract

We show that the weak solutions to the Navier–Stokes system exist, globally in time, for any finite energy initial data. The proof will be constructive in the sense that the desired weak solution is obtained as a suitable limit of a numerical scheme. By a numerical scheme we mean a finite number of algebraic equations yielding an approximate solution of the problem. To this end, we use the method of time discretization in combination with a mixed finite-volume finite-element scheme to solve that resulting “stationary” problems. The scheme is implicit, the numerical approximation at any time level is obtained as a solution of a finite system of nonlinear algebraic equations resulting from the spatial discretization.

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previous chapter Weak Sequential Stability
next chapter Stability of the Numerical Method
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Metadata
Title
Numerical Method
Authors
Eduard Feireisl
Trygve G. Karper
Milan Pokorný
Copyright Year
2016
Book
Mathematical Theory of Compressible Viscous Fluids

Print ISBN: 978-3-319-44834-3

Electronic ISBN: 978-3-319-44835-0

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-44835-0_7

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