Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows
Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows
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DOI：
10.1093/imanum/drm017
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发表时间：
2007-09
影响因子：
2.1
通讯作者：
S. Berrone;E. Süli
中科院分区：
文献类型：
--
作者：
S. Berrone;E. Süli
我们开发了一个后验的上下误差界混合有限元近似的一般家庭的稳定，粘性，不可压缩的拟牛顿流在一个有界Lipschitz域$\Omega \subset \mathbb{R}^d$;家庭包括退化模型，如幂律模型，以及非退化的，如Carreau模型。本文开发的统一的理论框架产生双边基于残差的后验界，其测量速度在$\WW^{1，r}（\Omega）$范数中的近似误差和压力在$\LL^{r '}（\Omega）$范数中的近似误差，$1/r+1/r'= 1$。
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, $1/r+1/r'=1$.