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Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows

Congreve, Scott; Houston, Paul; Süli, Endre; Wihler, Thomas P.

Authors

Scott Congreve pmxsc@nottingham.ac.uk

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Endre Süli Endre.Suli@maths.ox.ac.uk

Thomas P. Wihler wihler@math.unibe.ch



Abstract

In this article we develop both the a priori and a posteriori error analysis of hp– version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain Ω ⊂ R^d, d = 2, 3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp–adaptive refinement algorithm.

Citation

Congreve, S., Houston, P., Süli, E., & Wihler, T. P. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows. Manuscript submitted for publication

Journal Article Type Article
Deposit Date Jan 27, 2012
Journal IMA Journal of Numerical Analysis
Print ISSN 0272-4979
Electronic ISSN 0272-4979
Publisher Oxford University Press (OUP)
Peer Reviewed Not Peer Reviewed
Public URL http://eprints.nottingham.ac.uk/id/eprint/1565
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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