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Zbl 0916.76066
Wardi, S.
A convergence result for an iterative method for the equations of a stationary quasi-Newtonian flow with temperature dependent viscosity. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 32, No.4, 391-404 (1998). ISSN 0764-583X

Summary: We study a system of equations describing the stationary incompressible flow of a quasi-Newtonian fluid with temperature dependent viscosity and with a viscous heating. An algorithm which decouples the calculation of the temperature $T$ and the velocity and the pressure $(v,p)$ is presented. It consists in solving iteratively a problem with a nonlinear Stokes operator for $v$ and $p$, and the Poisson equation with right-hand side in $L^1$ for $T$. We prove, using the method of pseudomonotonicity and under a regularity assumption of Meyers type, that the mapping defined by this scheme is a contraction for sufficiently small data.

MSC 2000:: *76M25 Other numerical methods
76A05 Non-Newtonian fluids
65N12 Stability and convergence of numerical methods (BVP of PDE)
80A20 Heat and mass transfer

Keywords: contracting mapping; viscous heating; nonlinear Stokes operator; Poisson equation; method of pseudomonotonicity; regularity assumption

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