A Locally Adapting Parameter Design for the Divergence Stabilization of FEM Discretizations of the Navier-Stokes Equations

Abstract

We will first briefly summarize the previous efforts in constructing a parameter design for local projection and grad-div stabilization based on a-priori convergence analysis for the linearized problem given in [LRL08] and [MT07]. Especially for Taylor-Hood type elements this leads to a grad-div stabilization parameter μ ~ 1. While this design works well for some academic testproblems it does not give satisfactory results for others. A review of the convergence estimate suggests an aposteriori parameter design including local norms of velocity and pressure. Some first numerical results based on this parameter design will be presented.