Quasi-norm error bounds for the finite element approximation of a non- Newtonian flow. (English) Zbl 0811.76036

Barrett, John W.; Liu, W. B.

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.

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