Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows
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, a...
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| Format: | Report |
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Unspecified
2006
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| Summary: | 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, $1/r+1/r'=1$. |
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