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Durán, R.G.; Hernández, E.; Hervella-Nieto, L.; Liberman, E.; Rodríguezh, R. "Error estimates for low-order isoparametric quadrilateral finite elements for plates" (2003) SIAM Journal on Numerical Analysis. 41(5):1751-1772
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Abstract:

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.

Registro:

Documento: Artículo
Título:Error estimates for low-order isoparametric quadrilateral finite elements for plates
Autor:Durán, R.G.; Hernández, E.; Hervella-Nieto, L.; Liberman, E.; Rodríguezh, R.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
Departamento de Matemática, Univ. Tec. Federico S. Maria, Casilla 110-V, Valparaíso, Chile
Departamento de Matemáticas, Universidade da Coruña, 15071 - A Coruña, Spain
Comn. Invest. Cie. Provincia B.A., Departamento de Matemática, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina
GI2MA, Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Palabras clave: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
Año:2003
Volumen:41
Número:5
Página de inicio:1751
Página de fin:1772
DOI: http://dx.doi.org/10.1137/S0036142902409410
Título revista:SIAM Journal on Numerical Analysis
Título revista abreviado:SIAM J Numer Anal
ISSN:00361429
CODEN:SJNAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v41_n5_p1751_Duran

Referencias:

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Citas:

---------- APA ----------
Durán, R.G., Hernández, E., Hervella-Nieto, L., Liberman, E. & Rodríguezh, R. (2003) . Error estimates for low-order isoparametric quadrilateral finite elements for plates. SIAM Journal on Numerical Analysis, 41(5), 1751-1772.
http://dx.doi.org/10.1137/S0036142902409410
---------- CHICAGO ----------
Durán, R.G., Hernández, E., Hervella-Nieto, L., Liberman, E., Rodríguezh, R. "Error estimates for low-order isoparametric quadrilateral finite elements for plates" . SIAM Journal on Numerical Analysis 41, no. 5 (2003) : 1751-1772.
http://dx.doi.org/10.1137/S0036142902409410
---------- MLA ----------
Durán, R.G., Hernández, E., Hervella-Nieto, L., Liberman, E., Rodríguezh, R. "Error estimates for low-order isoparametric quadrilateral finite elements for plates" . SIAM Journal on Numerical Analysis, vol. 41, no. 5, 2003, pp. 1751-1772.
http://dx.doi.org/10.1137/S0036142902409410
---------- VANCOUVER ----------
Durán, R.G., Hernández, E., Hervella-Nieto, L., Liberman, E., Rodríguezh, R. Error estimates for low-order isoparametric quadrilateral finite elements for plates. SIAM J Numer Anal. 2003;41(5):1751-1772.
http://dx.doi.org/10.1137/S0036142902409410