Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations
The nonconforming mixed finite element methods (NMFEMs) are introduced and analyzed for the numerical discretization of a nonlinear, fully coupled stationary incompressible magnetohydrodynamics (MHD) problem in 3D. A family of the low-order elements on tetrahedra or hexahedra are chosen to approxima...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/825609 |
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| author | Dongyang Shi Zhiyun Yu |
| author_facet | Dongyang Shi Zhiyun Yu |
| author_sort | Dongyang Shi |
| collection | DOAJ |
| description | The nonconforming mixed finite element methods (NMFEMs) are introduced and analyzed for the numerical discretization of a nonlinear, fully coupled stationary incompressible magnetohydrodynamics (MHD) problem in 3D. A family of the low-order elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field, and the magnetic field. The existence and uniqueness of the approximate solutions are shown, and the optimal error estimates for the corresponding unknown variables in L2-norm are established, as well as those in a broken
H1-norm for the velocity and the magnetic fields. Furthermore, a new approach is adopted to prove the discrete Poincaré-Friedrichs inequality, which is easier than that of the previous literature. |
| format | Article |
| id | doaj-art-3a6f56d68eaf4a4ab968e424ee76e4cd |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-3a6f56d68eaf4a4ab968e424ee76e4cd2025-08-20T03:35:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/825609825609Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics EquationsDongyang Shi0Zhiyun Yu1Department of Mathematics, Zhengzhou University, Zhengzhou 450052, ChinaDepartment of Mathematics, Zhengzhou University, Zhengzhou 450052, ChinaThe nonconforming mixed finite element methods (NMFEMs) are introduced and analyzed for the numerical discretization of a nonlinear, fully coupled stationary incompressible magnetohydrodynamics (MHD) problem in 3D. A family of the low-order elements on tetrahedra or hexahedra are chosen to approximate the pressure, the velocity field, and the magnetic field. The existence and uniqueness of the approximate solutions are shown, and the optimal error estimates for the corresponding unknown variables in L2-norm are established, as well as those in a broken H1-norm for the velocity and the magnetic fields. Furthermore, a new approach is adopted to prove the discrete Poincaré-Friedrichs inequality, which is easier than that of the previous literature.http://dx.doi.org/10.1155/2012/825609 |
| spellingShingle | Dongyang Shi Zhiyun Yu Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations Journal of Applied Mathematics |
| title | Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations |
| title_full | Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations |
| title_fullStr | Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations |
| title_full_unstemmed | Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations |
| title_short | Low-Order Nonconforming Mixed Finite Element Methods for Stationary Incompressible Magnetohydrodynamics Equations |
| title_sort | low order nonconforming mixed finite element methods for stationary incompressible magnetohydrodynamics equations |
| url | http://dx.doi.org/10.1155/2012/825609 |
| work_keys_str_mv | AT dongyangshi lowordernonconformingmixedfiniteelementmethodsforstationaryincompressiblemagnetohydrodynamicsequations AT zhiyunyu lowordernonconformingmixedfiniteelementmethodsforstationaryincompressiblemagnetohydrodynamicsequations |