Dr. Blanca Ayuso

Postprocessing Mixed Finite Element Methods for the Navier-Stokes Equations.

(joint work with B. Garcia-Archilla & J. Novo)



Abstract:
In recent years, it was introduced a postprocessing technique based on the idea of Approximate Inertial Manifolds(AIMs). The technique was first developed for spectral methods and then, considered for standard finite-element methods for dissipative partial differential equations.

In this talk we shall extend the technique for the mixed finite element methods(MFEM) for the incompressible Navier-Stokes Equations.
We shall show that it enhances the accuracy and increase the efficiency of the MFEM. Accuracy is
enhanced by increasing the order of convergence of the velocity and pressure approximations. Efficiency is
enhanced since the postprocessing amounts to solving a single Stokes problem, once the time
integration(the most time consuming work) is completed.
We shall present some numerical experiments  that confirm both this increase in
the convergence rate and the corresponding improvement in
computational efficiency.