Barrett, John W.; Liu, W. B. Quasi-norm error bounds for the finite element approximation of a non- Newtonian flow. (English) Zbl 0811.76036 Numer. Math. 68, No. 4, 437-456 (1994). 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. Cited in 47 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76A05 Non-Newtonian fluids 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:Carreau law; power law; energy type error bounds; degenerate problems PDF BibTeX XML Cite \textit{J. W. Barrett} and \textit{W. B. Liu}, Numer. Math. 68, No. 4, 437--456 (1994; Zbl 0811.76036) Full Text: DOI OpenURL