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：本文提出一种新的有限元方法，以较低代价求解不可压缩斯托克斯方程中的$P^4$-速度和$P^3$-压力。该方法首先求解$P^4$-速度的解耦方程，然后利用计算所得速度，以分量方式定义局部可计算的$P^3$-压力。分析表明，该$P^3$-压力具有最优收敛阶。由于压力仅通过局部计算获得，新方法的主要时间开销在于求解$P^4$-速度的解耦方程。此外，该方法克服了奇异顶点或角点问题。