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Oxford University Press, IMA Journal of Numerical Analysis, 4(33), p. 1386-1415, 2013

DOI: 10.1093/imanum/drs046

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

Journal article published in 2011 by Scott Congreve, Paul Houston, Endre Suli ORCID, Thomas P. Wihler
This paper is available in a repository.
This paper is available in a repository.

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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.