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This paper will suggest a new finite element method to find a $P^4$-velocityand a $P^3$-pressure solving Stokes equations. The method solves first thedecoupled equation for the $P^4$-velocity. Then, four kinds of local$P^3$-pressures and one $P^0$-pressure will be calculated in a successive way.If we superpose them, the resulting $P^3$-pressure shows the optimal order ofconvergence same as a $P^3$-projection. The chief time cost of the new methodis on solving two linear systems for the $P^4$-velocity and $P^0$-pressure,respectively.

Successive finite element methods for Stokes equations