Mixed Quasi-Compressibility Methods

Overview

In the Chapters 3 and 4, we have been concerned with stationary and nonstationary quasi-compressibility methods in order to approximate the solutions of the incompressible (Navier-) Stokes equations. The drawback of non-stationary methods is that the corresponding finite element discretization schemes are only stable under certain restrictions F(ε, h, k) ≥ 0, for tuples of ansatz spaces that do not satisfy the LBB constraint. This prevents the applicability of the numerical scheme for the simulation of quickly varying space and time features of the solution. Therefore, we are naturally led to the investigation of so-called mixed quasi-compressibility methods. These schemes are composed of both stationary as well as nonstationary perturbation parts in the resulting quasi-compressibility scheme.