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EDP Sciences, ESAIM: Mathematical Modelling and Numerical Analysis, 7(32), p. 843-858

DOI: 10.1051/m2an/1998320708431

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A priori and a posteriori error bounds for a nonconforming linear finite element approximation of a non-newtonian flow

Journal article published in 1998 by Weizhu Bao ORCID, John W. Barrett
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We consider a nonconforming linear finite element approximation of a non-Newtonian flow, where the viscosity obeys a Carreau-type law for a pseudo-plastic fluid. We prove optimal a priori error bounds for velocity and pressure. In addition, we present a posteriori error estimators which are based on the local evaluation of the residuals. These yield global upper and local lower bounds for the error. Finally, we perform some numerical experiments which confirm a priori error bounds.