Workshop on Numerical Methods and Analysis in CFD - Abstract

García-Archilla, Bosco

Robust error bounds for the Navier--Stokes equations using implicit-explicit second order BDF method with variable steps

We present the analysis and numerical experimentation of a fully discrete method for the Navier-Stokes equations, using inf-sup stable elements and grad-div stabilization. For the time integration, the second order backward differentiation formula (BDF) with variable step sizes is used. We consider the cases where the nonlinear terms are treated explicitly and semi implicitly. Grad-div stabilization allows to obtain error bounds where the constants involved do not depend on the Reynolds number. When the nonlinear terms are treated explicitly, the resulting method suffers from a CFL-type restriction which can be checked in practical examples.