A locally calculable $P^3$-pressure using a $P^4$-velocity for incompressible Stokes equations

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, a $P^3$-pressure will be defined by locally calculable components. The resulting $P^3$-pressure shows the optimal order of convergence. 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.