Numerical approximation of an optimal control problem associated with the Navier-Stokes equations
The control problem consists of minimizing the cost \[ J(g)=\int_{\Omega}| u-u_ 0|^ 2+\int_{\Gamma}| g|^ 2 \] where the dynamics are given by the Navier-Stokes problem: -v \(\Delta u+(u\cdot \nabla)u+\nabla p=0\), \(\nabla \cdot u=0\), \(- pn+v(\nabla u+\nabla u^ T)n=g\) on \(\Gamma\). The problem is discussed from a numerical point of view using finite element approximations for the weak formulation of the dynamics.
scientific article; zbMATH DE number 4201021