A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems
The disproportionality in the problem parameters of the convection-diffusion-reaction equation may lead to the formation of layer structures in some parts of the problem domain which are difficult to resolve by the standard numerical algorithms. Therefore the use of a stabilized numerical method is...
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Wiley
2018-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2018/4259634 |
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| author | Ali Sendur |
| author_facet | Ali Sendur |
| author_sort | Ali Sendur |
| collection | DOAJ |
| description | The disproportionality in the problem parameters of the convection-diffusion-reaction equation may lead to the formation of layer structures in some parts of the problem domain which are difficult to resolve by the standard numerical algorithms. Therefore the use of a stabilized numerical method is inevitable. In this work, we employ and compare three classical stabilized finite element formulations, namely, the Streamline-Upwind Petrov-Galerkin (SUPG), Galerkin/Least-Squares (GLS), and Subgrid Scale (SGS) methods, and a recent Link-Cutting Bubble (LCB) strategy proposed by Brezzi and his coworkers for the numerical solution of the convection-diffusion-reaction equation, especially in the case of small diffusion. On the other hand, we also consider the pseudo residual-free bubble (PRFB) method as another alternative that is based on enlarging the finite element space by a set of appropriate enriching functions. We compare the performances of these stabilized methods on several benchmark problems. Numerical experiments show that the proposed methods are comparable and display good performance, especially in the convection-dominated regime. However, as the problem turns into reaction-dominated case, the PRFB method is slightly better than the other well-known and extensively used stabilized finite element formulations as they start to exhibit oscillations. |
| format | Article |
| id | doaj-art-b4e83cbaca28479bbbc5977c11987b3c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b4e83cbaca28479bbbc5977c11987b3c2025-02-03T05:46:14ZengWileyJournal of Applied Mathematics1110-757X1687-00422018-01-01201810.1155/2018/42596344259634A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction ProblemsAli Sendur0Alanya Alaaddin Keykubat University, 07490 Antalya, TurkeyThe disproportionality in the problem parameters of the convection-diffusion-reaction equation may lead to the formation of layer structures in some parts of the problem domain which are difficult to resolve by the standard numerical algorithms. Therefore the use of a stabilized numerical method is inevitable. In this work, we employ and compare three classical stabilized finite element formulations, namely, the Streamline-Upwind Petrov-Galerkin (SUPG), Galerkin/Least-Squares (GLS), and Subgrid Scale (SGS) methods, and a recent Link-Cutting Bubble (LCB) strategy proposed by Brezzi and his coworkers for the numerical solution of the convection-diffusion-reaction equation, especially in the case of small diffusion. On the other hand, we also consider the pseudo residual-free bubble (PRFB) method as another alternative that is based on enlarging the finite element space by a set of appropriate enriching functions. We compare the performances of these stabilized methods on several benchmark problems. Numerical experiments show that the proposed methods are comparable and display good performance, especially in the convection-dominated regime. However, as the problem turns into reaction-dominated case, the PRFB method is slightly better than the other well-known and extensively used stabilized finite element formulations as they start to exhibit oscillations.http://dx.doi.org/10.1155/2018/4259634 |
| spellingShingle | Ali Sendur A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems Journal of Applied Mathematics |
| title | A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems |
| title_full | A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems |
| title_fullStr | A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems |
| title_full_unstemmed | A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems |
| title_short | A Comparative Study on Stabilized Finite Element Methods for the Convection-Diffusion-Reaction Problems |
| title_sort | comparative study on stabilized finite element methods for the convection diffusion reaction problems |
| url | http://dx.doi.org/10.1155/2018/4259634 |
| work_keys_str_mv | AT alisendur acomparativestudyonstabilizedfiniteelementmethodsfortheconvectiondiffusionreactionproblems AT alisendur comparativestudyonstabilizedfiniteelementmethodsfortheconvectiondiffusionreactionproblems |