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

Wihler, Thomas; Congreve, Scott Spencer; Süli, E. (2013). Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows. IMA journal of numerical analysis, 33(4), pp. 1386-1415. Oxford University Press 10.1093/imanum/drs046

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In this article, we develop 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 ⊂ ℝd, 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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Wihler, Thomas and Congreve, Scott Spencer

Subjects:

500 Science > 510 Mathematics

ISSN:

0272-4979

Publisher:

Oxford University Press

Language:

English

Submitter:

Mario Amrein

Date Deposited:

28 Feb 2014 09:34

Last Modified:

27 Apr 2018 09:13

Publisher DOI:

10.1093/imanum/drs046

BORIS DOI:

10.7892/boris.41928

URI:

https://boris.unibe.ch/id/eprint/41928

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