Workshop on Numerical Methods and Analysis in CFD - Abstract

Park, Chunjae

Local computation of pressure in high order finite element methods for Stokes equations

We will suggest a new economic high-order finite element method for Stokes equations. Its main character is the local computation for the pressure. For an example, in P⁴ --- P³ case, the method solves first the decoupled equation for a P⁴-velocity. Then, a P³-pressure p_h is calculated by local computation in the successive 5 steps. The resulting P³-pressure is analyzed to have the optimal order O(h⁴) of convergence. Besides, the method overcomes the singular vertex annoying us in Scott--Vogelius finite element methods.