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

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):= u_x v_y - u_y v_x.

This paper is the abridged version of the author’s Habilitationsschrift.