Numerical approximation of generalized Newtonian fluids using Powell-Sabin-Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method o...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2003-04, Vol.41 (10), p.1085-1118
Main Authors: Chow, S.-S., Carey, G. F.
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
divergence free elements
error estimates
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Non-newtonian fluid flows
non-Newtonian fluids
Physics
Powell-Sabin-Heindl bases
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Summary:In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.480