Numerische Mathematik

, Volume 68, Issue 4, pp 437-456

First online:

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

  • John W. BarrettAffiliated withDepartment of Mathematics, Imperial College, London SW7 2BZ, UK
  • , W.B. LiuAffiliated withDepartment of Mathematics, Imperial College, London SW7 2BZ, UK

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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.

Mathematics Subject Classification (1991): 65N30