  In 1991 Ramshaw and Mesina introduced a clever synthesis of penalty methods
and artificial compression methods. Its form makes it an interesting option to
replace the pressure update in the Uzawa iteration. The result, for the Stokes
problem, is \begin{equation} \left\{ \begin{array} [c]{cc} Step\ 1: &
-\triangle u^{n+1}+\nabla p^{n}=f(x),\ {\rm in}\ \Omega,\
u^{n+1}|_{\partial\Omega}=0,\\ Step\ 2: &
p^{n+1}-p^{n}+\beta\nabla\cdot(u^{n+1}-u^{n})+\alpha ^{2}\nabla\cdot u^{n+1}=0.
\end{array} \right. \end{equation} For saddle point problems, including Stokes,
this iteration converges under a condition similar to the one required for
Uzawa iteration.
