Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows
In this article we consider the a priori and a posteriori error analysis of two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a strongly monotone quasi-Newtonian fluid flow problem. The basis of the two-grid method is to first solve the underlying nonlin...
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Institute for Scientific Computing and Information
2014
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| Online Access: | https://eprints.nottingham.ac.uk/29671/ |
| _version_ | 1848793827439017984 |
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| author | Congreve, Scott Houston, Paul |
| author_facet | Congreve, Scott Houston, Paul |
| author_sort | Congreve, Scott |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the a priori and a posteriori error analysis of two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a strongly monotone quasi-Newtonian fluid flow problem. The basis of the two-grid method is to first solve the underlying nonlinear problem on a coarse finite element space; a fine grid solution is then computed based on undertaking a suitable linearization of the discrete problem. Here, we study two alternative linearization techniques: the first approach involves evaluating the nonlinear viscosity coefficient using the coarse grid solution, while the second method utilizes an incomplete Newton iteration technique. Energy norm error bounds are deduced for both approaches. Moreover, we design an hp-adaptive refinement strategy in order to automatically design the underlying coarse and fine finite element spaces. Numerical experiments are presented which demonstrate the practical performance of both two-grid discontinuous Galerkin methods. |
| first_indexed | 2025-11-14T19:06:29Z |
| format | Article |
| id | nottingham-29671 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:06:29Z |
| publishDate | 2014 |
| publisher | Institute for Scientific Computing and Information |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-296712020-05-04T20:16:16Z https://eprints.nottingham.ac.uk/29671/ Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows Congreve, Scott Houston, Paul In this article we consider the a priori and a posteriori error analysis of two-grid hp-version discontinuous Galerkin finite element methods for the numerical solution of a strongly monotone quasi-Newtonian fluid flow problem. The basis of the two-grid method is to first solve the underlying nonlinear problem on a coarse finite element space; a fine grid solution is then computed based on undertaking a suitable linearization of the discrete problem. Here, we study two alternative linearization techniques: the first approach involves evaluating the nonlinear viscosity coefficient using the coarse grid solution, while the second method utilizes an incomplete Newton iteration technique. Energy norm error bounds are deduced for both approaches. Moreover, we design an hp-adaptive refinement strategy in order to automatically design the underlying coarse and fine finite element spaces. Numerical experiments are presented which demonstrate the practical performance of both two-grid discontinuous Galerkin methods. Institute for Scientific Computing and Information 2014 Article PeerReviewed Congreve, Scott and Houston, Paul (2014) Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows. International Journal of Numerical Analysis and Modeling, 11 (3). pp. 496-524. ISSN 1705-5105 hp-finite element methods; discontinuous Galerkin methods a posteriori error estimation adaptivity two-grid methods non-Newtonian fluids http://www.math.ualberta.ca/ijnam/Volume11.htm |
| spellingShingle | hp-finite element methods; discontinuous Galerkin methods a posteriori error estimation adaptivity two-grid methods non-Newtonian fluids Congreve, Scott Houston, Paul Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title | Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title_full | Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title_fullStr | Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title_full_unstemmed | Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title_short | Two-grid hp-version discontinuous Galerkin finite element methods for quasi-Newtonian fluid flows |
| title_sort | two-grid hp-version discontinuous galerkin finite element methods for quasi-newtonian fluid flows |
| topic | hp-finite element methods; discontinuous Galerkin methods a posteriori error estimation adaptivity two-grid methods non-Newtonian fluids |
| url | https://eprints.nottingham.ac.uk/29671/ https://eprints.nottingham.ac.uk/29671/ |