An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities
The Uzawa method is an iterative approach to find approximated solutions to the Stokes equations. This method solves velocity variables involving augmented Lagrangian operator and then updates pressure variable by Richardson update. In this paper, we construct a new version of the Uzawa method to fi...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5592982 |
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| author | Jae-Hong Pyo Deok-Kyu Jang |
| author_facet | Jae-Hong Pyo Deok-Kyu Jang |
| author_sort | Jae-Hong Pyo |
| collection | DOAJ |
| description | The Uzawa method is an iterative approach to find approximated solutions to the Stokes equations. This method solves velocity variables involving augmented Lagrangian operator and then updates pressure variable by Richardson update. In this paper, we construct a new version of the Uzawa method to find optimal numerical solutions of the Stokes equations including corner singularities. The proposed method is based on the dual singular function method which was developed for elliptic boundary value problems. We estimate the solvability of the proposed formulation and special orthogonality form for two singular functions. Numerical convergence tests are presented to verify our assertion. |
| format | Article |
| id | doaj-art-3b3b08942e724ff3a0c4f6e3cc490b1c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-3b3b08942e724ff3a0c4f6e3cc490b1c2025-08-20T03:55:36ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55929825592982An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner SingularitiesJae-Hong Pyo0Deok-Kyu Jang1Department of Mathematics, Kangwon National University, Chuncheon 24341, Republic of KoreaDepartment of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of KoreaThe Uzawa method is an iterative approach to find approximated solutions to the Stokes equations. This method solves velocity variables involving augmented Lagrangian operator and then updates pressure variable by Richardson update. In this paper, we construct a new version of the Uzawa method to find optimal numerical solutions of the Stokes equations including corner singularities. The proposed method is based on the dual singular function method which was developed for elliptic boundary value problems. We estimate the solvability of the proposed formulation and special orthogonality form for two singular functions. Numerical convergence tests are presented to verify our assertion.http://dx.doi.org/10.1155/2021/5592982 |
| spellingShingle | Jae-Hong Pyo Deok-Kyu Jang An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities Journal of Mathematics |
| title | An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities |
| title_full | An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities |
| title_fullStr | An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities |
| title_full_unstemmed | An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities |
| title_short | An Optimal Finite Element Method with Uzawa Iteration for Stokes Equations including Corner Singularities |
| title_sort | optimal finite element method with uzawa iteration for stokes equations including corner singularities |
| url | http://dx.doi.org/10.1155/2021/5592982 |
| work_keys_str_mv | AT jaehongpyo anoptimalfiniteelementmethodwithuzawaiterationforstokesequationsincludingcornersingularities AT deokkyujang anoptimalfiniteelementmethodwithuzawaiterationforstokesequationsincludingcornersingularities AT jaehongpyo optimalfiniteelementmethodwithuzawaiterationforstokesequationsincludingcornersingularities AT deokkyujang optimalfiniteelementmethodwithuzawaiterationforstokesequationsincludingcornersingularities |