Successive finite element methods for Stokes equations

Abstract: This paper will suggest a new finite element method to find a $P^4$-velocity and a $P^3$-pressure solving Stokes equations. The method solves first the decoupled 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 of convergence same as a $P^3$-projection. The chief time cost of the new method is on solving two linear systems for the $P^4$-velocity and $P^0$-pressure, respectively.