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Computation of Turning Points of the Stationary Navier-Stokes Equations Using Mixed Finite Elements

  • Reinhard Scholz
Chapter
Part of the ISNM: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 54)

Abstract

As a model problem we consider the stationary Navier-Stokes equations in a bounded and simply connected domain Ω⊆R2 with sufficiently smooth boundary. These equations can be transformed into a fourth order boundary value problem
$$[tex]\begin{array}{*{20}{c}}{v{\Delta ^2}u + A(u,\Delta u) = f\quad in\quad \Omega } \\{\left. {\begin{array}{*{20}{c}}{u = {g_1}}\\{\frac{{\partial u}}{{\partial n}} = {g_2}}\\\end{array}} \right\}\quad on\quad \partial \Omega }\\\end{array}[/tex]$$
with a quadratic nonlinearity A(u,v):= ux vy - uy vx.

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Copyright information

© Springer Basel AG 1980

Authors and Affiliations

  • Reinhard Scholz
    • 1
  1. 1.Institut für Angewandte MathematikAlbert-Ludwigs-UniversitätFreiburgFederal Republic of Germany

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