Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows

Report

We develop a posteriori upper and lower error bounds for mixed finite element approximations of a general family of steady, viscous, incompressible quasi-Newtonian flows in a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$; the family includes degenerate models such as the power-law model, as well as non-degenerate ones such as the Carreau model. The unified theoretical framework developed herein yields two-sided residual-based a posteriori bounds which measure the error in the approximation of the velocity in the $\WW^{1,r}(\Omega)$ norm and that of the pressure in the $\LL^{r'}(\Omega)$ norm, $1/r+1/r'=1$.

Authors: Berrone, S; Suli, E

• Publisher: Unspecified
• Publication date: 2006-06-01