, Volume 68, Issue 4, pp 437-456

Quasi-norm error bounds for the finite element approximation of a non-Newtonian flow

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Summary.

We consider the finite element approximation of a non-Newtonian flow, where the viscosity obeys a general law including the Carreau or power law. For sufficiently regular solutions we prove energy type error bounds for the velocity and pressure. These bounds improve on existing results in the literature. A key step in the analysis is to prove abstract error bounds initially in a quasi-norm, which naturally arises in degenerate problems of this type.

Received May 25, 1993 / Revised version received January 11, 1994