Mixed FEM for the Stokes problem#
We consider now the Stokes problem for the steady-state modelling of an incompressible fluid
\[\begin{split}
\begin{align}
\left\{
\begin{array}{rl}
- \nabla^2 \mathbf{u} + \nabla p = \mathbf{f} & \mbox{in} ~ \Omega, \\
\nabla \cdot \mathbf{u} = 0 & \mbox{in} ~ \Omega, \\
\mathbf{u} = 0 & \mbox{on} ~ \partial \Omega,
\end{array}
\right.
\end{align}
\end{split}\]