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.

翻译：1991年，Ramshaw和Mesina提出了一种罚函数法与人工压缩法的巧妙结合。该迭代形式使其成为替代Uzawa迭代中压力更新的有趣选择。针对Stokes问题，该迭代格式为： \begin{equation} \left\{ \begin{array} [c]{cc} 步骤1: & -\triangle u^{n+1}+\nabla p^{n}=f(x),\ {\rm in}\ \Omega,\ u^{n+1}|_{\partial\Omega}=0,\\ 步骤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} 对于包括Stokes问题在内的鞍点问题，该迭代在类似于Uzawa迭代所需条件的约束下收敛。