An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations
We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1−P0 and P1−P0). Firstly, in contrast to other stabilized methods, they are parameter fre...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/520818 |
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| author | Aiwen Wang Xin Zhao Peihua Qin Dongxiu Xie |
| author_facet | Aiwen Wang Xin Zhao Peihua Qin Dongxiu Xie |
| author_sort | Aiwen Wang |
| collection | DOAJ |
| description | We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1−P0 and P1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, a large general Stokes equation on the fine mesh with mesh size h=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations. |
| format | Article |
| id | doaj-art-6e600f66aef546e3862aed19dd9faf85 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6e600f66aef546e3862aed19dd9faf852025-02-03T01:10:45ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/520818520818An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes EquationsAiwen Wang0Xin Zhao1Peihua Qin2Dongxiu Xie3Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, ChinaDepartement of Geographical Science and Environmental Engineering, Baoji University of Arts and Sciences, Baoji 721007, ChinaInstitute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, ChinaSchool of Applied Science, Beijing Information Science and Technology University, Beijing 100192, ChinaWe investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1−P0 and P1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, a large general Stokes equation on the fine mesh with mesh size h=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.http://dx.doi.org/10.1155/2012/520818 |
| spellingShingle | Aiwen Wang Xin Zhao Peihua Qin Dongxiu Xie An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations Abstract and Applied Analysis |
| title | An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations |
| title_full | An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations |
| title_fullStr | An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations |
| title_full_unstemmed | An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations |
| title_short | An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations |
| title_sort | oseen two level stabilized mixed finite element method for the 2d 3d stationary navier stokes equations |
| url | http://dx.doi.org/10.1155/2012/520818 |
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