This paper will suggest a new finite element method to find a $P^4$-velocity and a $P^3$-pressure solving incompressible Stokes equations at low cost. The method solves first the decoupled equation for a $P^4$-velocity. Then, using the calculated velocity, a locally calculable $P^3$-pressure will be defined component-wisely. The resulting $P^3$-pressure is analyzed to have the optimal order of convergence. Since the pressure is calculated by local computation only, the chief time cost of the new method is on solving the decoupled equation for the $P^4$-velocity. Besides, the method overcomes the problem of singular vertices or corners.
翻译：本文将建议一种新的有限要素方法, 以寻找 $P 4$- 速度和 $P 3$- 压力解压缩 斯托克斯 方程式, 低成本。 该方法首先解析 $P 4$- 速度的分离方程式 。 然后, 使用计算速度, 本地可计算 $P 3$- 压力 将会被定义为元件。 由此得出的 $P 3$- 压力将分析为最佳趋同顺序 。 由于压力仅由本地计算计算, 新方法的主要时间成本是解决 $P 4$ 速度的分离方程式 。 此外, 该方法克服了单项脊椎或角的问题 。
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