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Nonlinear Problems

  • Joël ChaskalovicEmail author
Chapter
  • 2.8k Downloads
Part of the Mathematical Engineering book series (MATHENGIN)

Abstract

We begin this section with a warning. We discuss here the viscous Burgers equation as an approximation to the Navier–Stokes equation in one space dimension. In order to focus on a mixed formulation considering a finite-element analysis in space and a finite-difference analysis in time that will be accessible to students at the beginning graduate level who have not yet mastered the functional analysis required for the resulting treatment, the following presentation contains no consideration of the necessary functional framework. In other words, we discuss only formal features of the variational formulations and numerical implementation of the finite-element analysis.

Keywords

Viscous Burgers Equation Strict Node Approximate Variational Formulation Repeated Index Convention Real-valued Test Functions 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    D. Euvrard, Résolution des équations aux dérivées partielles de la physique, de la mécanique et des sciences de l’ingénieur (Masson, Paris, 1994)Google Scholar
  2. 2.
    P.A. Raviart, E. Godlewski, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Appl. Math. Sci., 118 (Springer, New York, 1996)Google Scholar
  3. 3.
    M. Crouzeix, A.L. Mignot, Analyse numérique des équations différentielles (Masson, Paris, 1983)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut Jean le Rond d’AlembertUniversity Pierre and Marie CurieParisFrance

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