A new stabilized method for quasi-Newtonian flows |
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Authors: | Chun-mei Xie Min-fu Feng |
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Institution: | 1. School of Applied Mathematics,University of Electronic Science and Technology of China,Chengdu 610054,P.R.China 2. School of Applied Mathematics,University of Electronic Science and Technology of China,Chengdu 610054,P.R.China;School of Mathematics,Sichuan University,Chengdu 610064,P.R.China |
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Abstract: | For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, (bi)linear/(bi)linear and (bi)linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in theW1,r(Ω) norm and that of the pressure in the Lr´(Ω) (1/r +1/r´ = 1). The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results. |
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Keywords: | quasi-Newtonian stabilized method power law model Carreau model residual-based posterior bound |
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