Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows
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...
| Main Authors: | , , , |
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| Format: | Article |
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Oxford University Press
2012
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| Online Access: | https://eprints.nottingham.ac.uk/1565/ |
| _version_ | 1848790630360154112 |
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| author | Congreve, Scott Houston, Paul Süli, Endre Wihler, Thomas P. |
| author_facet | Congreve, Scott Houston, Paul Süli, Endre Wihler, Thomas P. |
| author_sort | Congreve, Scott |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:15:40Z |
| format | Article |
| id | nottingham-1565 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:15:40Z |
| publishDate | 2012 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-15652020-05-04T20:22:21Z https://eprints.nottingham.ac.uk/1565/ 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. 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. Oxford University Press 2012 Article NonPeerReviewed Congreve, Scott, Houston, Paul, Süli, Endre and Wihler, Thomas P. (2012) Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows. IMA Journal of Numerical Analysis . ISSN 0272-4979 (Submitted) |
| spellingShingle | Congreve, Scott Houston, Paul Süli, Endre Wihler, Thomas P. Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title_full | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title_fullStr | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title_full_unstemmed | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title_short | Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: strongly monotone quasi-Newtonian flows |
| title_sort | discontinuous galerkin finite element approximation of quasilinear elliptic boundary value problems ii: strongly monotone quasi-newtonian flows |
| url | https://eprints.nottingham.ac.uk/1565/ |