Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows
We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-lev...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/698354 |
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| _version_ | 1832554354404491264 |
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| author | Rong An Xian Wang |
| author_facet | Rong An Xian Wang |
| author_sort | Rong An |
| collection | DOAJ |
| description | We present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods. |
| format | Article |
| id | doaj-art-57a508b4f52a433aacf2c6752852b43a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-57a508b4f52a433aacf2c6752852b43a2025-02-03T05:51:44ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/698354698354Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible FlowsRong An0Xian Wang1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaWe present a new stabilized finite element method for incompressible flows based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of finite element solutions are derived for classical one-level method. Combining the techniques of two-level discretizations, we propose two-level Stokes/Oseen/Newton iteration methods corresponding to three different linearization methods and show the stability and error estimates of these three methods. We also propose a new Newton correction scheme based on the above two-level iteration methods. Finally, some numerical experiments are given to support the theoretical results and to check the efficiency of these two-level iteration methods.http://dx.doi.org/10.1155/2014/698354 |
| spellingShingle | Rong An Xian Wang Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows Abstract and Applied Analysis |
| title | Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows |
| title_full | Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows |
| title_fullStr | Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows |
| title_full_unstemmed | Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows |
| title_short | Two-Level Brezzi-Pitkäranta Stabilized Finite Element Methods for the Incompressible Flows |
| title_sort | two level brezzi pitkaranta stabilized finite element methods for the incompressible flows |
| url | http://dx.doi.org/10.1155/2014/698354 |
| work_keys_str_mv | AT rongan twolevelbrezzipitkarantastabilizedfiniteelementmethodsfortheincompressibleflows AT xianwang twolevelbrezzipitkarantastabilizedfiniteelementmethodsfortheincompressibleflows |