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IMA Journal of Numerical Analysis Advance Access originally published online on September 19, 2007
IMA Journal of Numerical Analysis 2008 28(2):382-421; doi:10.1093/imanum/drm017
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Two-sided a posteriori error bounds for incompressible quasi-Newtonian flows

Stefano Berrone{dagger}

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy

Endre Süli{ddagger}

Computing Laboratory, University of Oxford, Parks Road, Oxford OX1 3QD, UK

{dagger} Email: sberrone{at}calvino.polito.it

{ddagger} Email: endre{at}comlab.ox.ac.uk

Received on 30 June 2006. Revised on 27 March 2007.


  Abstract

We develop a posteriori upper and lower error bounds for mixed finite-element approximations of a general family of steady, viscous, incompressible quasi-Newtonian flows in a bounded Lipschitz domain Formula ; the family includes degenerate models such as the power law model, as well as non-degenerate ones such as the Carreau model. The unified theoretical framework developed herein yields residual-based a posteriori bounds which measure the error in the approximation of the velocity in the W1, r({Omega}) norm and that of the pressure in the Lr'({Omega}) norm, 1/r + 1/r' = 1, r isin (1, {infty}).

Key Words: finite-element methods; a posteriori error estimates; non-Newtonian fluids


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