Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions
This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with so...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/125139 |
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| _version_ | 1850106491091025920 |
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| author | Yuan Li Rong An |
| author_facet | Yuan Li Rong An |
| author_sort | Yuan Li |
| collection | DOAJ |
| description | This paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method. |
| format | Article |
| id | doaj-art-2e5abc8422e1483092d5f5971a2c5847 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2e5abc8422e1483092d5f5971a2c58472025-08-20T02:38:49ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/125139125139Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary ConditionsYuan Li0Rong An1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaCollege of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, ChinaThis paper presents two-level iteration penalty finite element methods to approximate the solution of the Navier-Stokes equations with friction boundary conditions. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size H in combining with solving a Stokes, Oseen, or linearized Navier-Stokes type variational inequality problem for Stokes, Oseen, or Newton iteration on a fine mesh with mesh size h. The error estimate obtained in this paper shows that if H, h, and ε can be chosen appropriately, then these two-level iteration penalty methods are of the same convergence orders as the usual one-level iteration penalty method.http://dx.doi.org/10.1155/2013/125139 |
| spellingShingle | Yuan Li Rong An Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions Abstract and Applied Analysis |
| title | Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions |
| title_full | Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions |
| title_fullStr | Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions |
| title_full_unstemmed | Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions |
| title_short | Two-Level Iteration Penalty Methods for the Navier-Stokes Equations with Friction Boundary Conditions |
| title_sort | two level iteration penalty methods for the navier stokes equations with friction boundary conditions |
| url | http://dx.doi.org/10.1155/2013/125139 |
| work_keys_str_mv | AT yuanli twoleveliterationpenaltymethodsforthenavierstokesequationswithfrictionboundaryconditions AT rongan twoleveliterationpenaltymethodsforthenavierstokesequationswithfrictionboundaryconditions |