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

Journal article

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; 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(Ω) norm and that of the pressure in the Lr′(Ω) norm, 1/r + 1/r′ = 1, r ∈ (1, ∞).

Authors: Berrone, S; Suli, E

• Publication status: Published
• Journal: IMA JOURNAL OF NUMERICAL ANALYSIS
• Volume: 28
• Issue: 2
• Pages: 382-421
• Publication date: 2008-04-01
• DOI: 10.1093/imanum/drrnO17
• EISSN: 1464-3642
• ISSN: 0272-4979
• Language: English
• Keywords: finite-element methods; a posteriori error estimates; non-Newtonian fluids