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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |