Error estimates for low-order isoparametric quadrilateral finite elements for plates
This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In parti...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00361429_v41_n5_p1751_Duran |
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todo:paper_00361429_v41_n5_p1751_Duran2023-10-03T14:47:43Z Error estimates for low-order isoparametric quadrilateral finite elements for plates Durán, R.G. Hernández, E. Hervella-Nieto, L. Liberman, E. Rodríguezh, R. Isoparametric quadrilaterals MITC methods Reissner-Mindlin Approximation theory Boundary conditions Convergence of numerical methods Finite element method Integration Interpolation Mathematical models Perturbation techniques Tensors Error estimation Isoparametric quadrilaterals Plate thickness Error analysis This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes. Under mild assumptions we obtain optimal H1 and L2 error estimates for both methods. These estimates are valid with constants independent of the plate thickness. We also obtain error estimates for the approximation of the plate vibration problem. Finally, we report some numerical experiments showing the very good behavior of the methods, even in some cases not covered by our theory. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00361429_v41_n5_p1751_Duran |
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Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Isoparametric quadrilaterals MITC methods Reissner-Mindlin Approximation theory Boundary conditions Convergence of numerical methods Finite element method Integration Interpolation Mathematical models Perturbation techniques Tensors Error estimation Isoparametric quadrilaterals Plate thickness Error analysis |
| spellingShingle |
Isoparametric quadrilaterals MITC methods Reissner-Mindlin Approximation theory Boundary conditions Convergence of numerical methods Finite element method Integration Interpolation Mathematical models Perturbation techniques Tensors Error estimation Isoparametric quadrilaterals Plate thickness Error analysis Durán, R.G. Hernández, E. Hervella-Nieto, L. Liberman, E. Rodríguezh, R. Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| topic_facet |
Isoparametric quadrilaterals MITC methods Reissner-Mindlin Approximation theory Boundary conditions Convergence of numerical methods Finite element method Integration Interpolation Mathematical models Perturbation techniques Tensors Error estimation Isoparametric quadrilaterals Plate thickness Error analysis |
| description |
This paper deals with the numerical approximation of the bending of a plate modeled by Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is based on the family of elements called MITC (mixed interpolation of tensorial components). We consider two lowest-order methods of this family on quadrilateral meshes. Under mild assumptions we obtain optimal H1 and L2 error estimates for both methods. These estimates are valid with constants independent of the plate thickness. We also obtain error estimates for the approximation of the plate vibration problem. Finally, we report some numerical experiments showing the very good behavior of the methods, even in some cases not covered by our theory. |
| format |
JOUR |
| author |
Durán, R.G. Hernández, E. Hervella-Nieto, L. Liberman, E. Rodríguezh, R. |
| author_facet |
Durán, R.G. Hernández, E. Hervella-Nieto, L. Liberman, E. Rodríguezh, R. |
| author_sort |
Durán, R.G. |
| title |
Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| title_short |
Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| title_full |
Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| title_fullStr |
Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| title_full_unstemmed |
Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| title_sort |
error estimates for low-order isoparametric quadrilateral finite elements for plates |
| url |
http://hdl.handle.net/20.500.12110/paper_00361429_v41_n5_p1751_Duran |
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