The Postprocessed Mixed Finite-Element Method for the Navier--Stokes Equations

Abstract

A postprocessing technique for mixed finite-element methods for the incompressible Navier–Stokes equations is studied. The technique was earlier developed for spectral and standard finite-element methods for dissipative partial differential equations. The postprocessing amounts to solving a Stokes problem on a finer grid (or higher-order space) once the time integration on the coarser mesh is completed. The analysis presented here shows that this technique increases the convergence rate of both the velocity and the pressure approximations. Numerical experiments are presented that confirm both this increase in the convergence rate and the corresponding improvement in computational efficiency.