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A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model

Hsueh-Chen Lee Wenzao Ursuline University of Languages

Numerical Analysis and Scientific Computing mathscidoc:1612.25003

Journal of Mathematical Analysis and Applications, 432, 844-861, 2015.12
We study a nonlinear weighted least-squares finite element method for the Navier- Stokes equations governing non-Newtonian fluid flows by using the Carreau- Yasuda model. The Carreau-Yasuda model is used to describe the shear-thinning behavior of blood. We prove that the least-squares approximation converges to linearized solutions of the non-Newtonian model at the optimal rate. By using continuous piecewise linear finite element spaces for all variables and by appropriately adjusting the nonlinear weighting function, we obtain optimal L2-norm error convergence rates in all variables. Numerical results are given for a Carreau fluid in the 4-to-1 contraction problem, revealing the shear-thinning behavior. The physical parameter effects are also investigated.
weighted least-squares; nonlinear weight; non-Newtonian;Carreau-Yasuda; shear-thinning
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@inproceedings{hsueh-chen2015a,
  title={A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model},
  author={Hsueh-Chen Lee},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161225155255531907690},
  booktitle={Journal of Mathematical Analysis and Applications},
  volume={432},
  pages={844-861},
  year={2015},
}
Hsueh-Chen Lee. A nonlinear weighted least-squares finite element method for the Carreau-Yasuda non-Newtonian model. 2015. Vol. 432. In Journal of Mathematical Analysis and Applications. pp.844-861. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161225155255531907690.
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