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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Society for Industrial and Applied Mathematics Publications
2003
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| LEADER | 08260caa a22008657a 4500 | ||
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| 001 | PAPER-4750 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203420.0 | ||
| 008 | 190411s2003 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-9244256739 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a SJNAA | ||
| 100 | 1 | |a Durán, R.G. | |
| 245 | 1 | 0 | |a Error estimates for low-order isoparametric quadrilateral finite elements for plates |
| 260 | |b Society for Industrial and Applied Mathematics Publications |c 2003 | ||
| 270 | 1 | 0 | |m Durán, R.G.; Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina; email: rduran@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Janabi, B.S.A.L., Hinton, E., A study of the free vibrations of square plates with various edge conditions (1988) Numerical Methods and Software for Dynamic Analysis of Plates and Shells, pp. 167-204. , E. Hinton, ed., Pineridge Press, Swansea, UK | ||
| 504 | |a Arnold, D.N., Falk, R.S., A uniformly accurate finite element method for the Reissner-Mindlin plate (1989) SIAM J. Numer. Anal., 26, pp. 1276-1290 | ||
| 504 | |a Arnold, D.N., Boffi, D., Falk, R.S., Approximation by quadrilateral finite elements (2002) Math. Comp., 71, pp. 909-922 | ||
| 504 | |a Arnold, D.N., Boffi, D., Falk, R.S., Gastaldi, L., Finite element approximation on quadrilateral meshes (2001) Comm. Numer. Methods Engrg., 17, pp. 805-812 | ||
| 504 | |a Babuška, I., Osborn, J., Eigenvalue problems (1991) Handbook of Numerical Analysis, 2, pp. 641-787. , P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam | ||
| 504 | |a Bathe, K.-J., Brezzi, F., On the convergence of o four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation (1985) The Mathematics of Finite Elements and Applications V, pp. 491-503. , J. R. Whiteman, ed., Academic Press, London | ||
| 504 | |a Bathe, K.-J., Dvorkin, E.N., A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation (1985) Internat. J. Numer. Methods Engrg., 21, pp. 367-383 | ||
| 504 | |a Bathe, K.-J., Iosilevich, A., Chapelle, D., An evaluation of the MITC shell elements (2000) Comput. & Structures, 75, pp. 1-30 | ||
| 504 | |a Brezzi, F., Fortin, M., (1991) Mixed and Hybrid Finite Element Methods, , Springer-Verlag, New York | ||
| 504 | |a Brezzi, F., Fortin, M., Stenberg, R., Quasi-optimal error bounds for approximation of shear-stresses in Mindlin-Reissner plate models (1991) Math. Models Methods Appl. Sci., 1, pp. 125-151 | ||
| 504 | |a Ciarlet, P.G., Basic error estimates for elliptic problems (1991) Handbook of Numerical Analysis, 2, pp. 17-351. , P. G. Ciarlet and J. L. Lions, eds., North-Holland, Amsterdam | ||
| 504 | |a Durán, R., Liberman, E., On mixed finite element methods for the Reissner-Mindlin plate model (1992) Math. Comp., 58, pp. 561-573 | ||
| 504 | |a Durán, R., Hervella-Nieto, L., Liberman, E., Rodrígues, R., Solomin, J., Approximation of the vibration modes of a plate by Reissner-Mindlin equations (1999) Math. Comp., 68, pp. 1447-1463 | ||
| 504 | |a Girault, V., Raviart, P.A., (1986) Finite Element Methods for Navier-stokes Equations, , Springer-Verlag, Berlin | ||
| 504 | |a Hernández, E., Hervella-Nieto, L., Rodríguez, R., Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elements (2003) Comput. & Structures, 81, pp. 615-628 | ||
| 504 | |a Kato, T., (1995) Perturbation Theory for Linear Operators, , Springer-Verlag, Berlin | ||
| 504 | |a Liberman, E., (1995) Sobre la Convergencia de Métodos de Elementos Finitos para el Modelo de Placas de Reissner-mindlin, , Ph.D. thesis, Universidad Nacional de La Plata, Argentina | ||
| 504 | |a Peisker, P., Braess, D., Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates (1992) M2AN Math. Model. Numer. Anal., 26, pp. 557-574 | ||
| 504 | |a Pitkäranta, J., Stenberg, R., Error bounds for the approximation of the Stokes problem using bilinear/constant elements on irregular quadrilateral meshes (1985) The Mathematics of Finite Elements and Applications V, pp. 325-334. , J. R. Whiteman, ed., Academic Press, London | ||
| 504 | |a Pitkäranta, J., Suri, M., Design principles and error analysis for reduced-shear plate-bending finite elements (1996) Numer. Math., 75, pp. 223-266 | ||
| 504 | |a Raviart, P.A., Thomas, J.M., A mixed finite element method for second order elliptic problems (1977) Lecture Notes in Mathematics, 606, pp. 292-315. , Mathematical Aspects of Finite Element Methods, I. Galligani and E. Magenes, eds., Springer-Verlag, Berlin | ||
| 504 | |a Stenberg, R., Analysis of mixed finite element methods for the Stokes problem: A unified approach (1984) Math. Comp., 42, pp. 9-23 | ||
| 504 | |a Stenberg, R., Suri, M., An hp error analysis of MITC plate elements (1997) SIAM J. Numer. Anal., 34, pp. 544-568 | ||
| 504 | |a Thomas, J.M., (1977) Sur l'Analyse Numérique des Méthodes d'Éléments Finis Hybrides et Mixtes, , Thèse de Doctorat d'Etat, Université Pierre et Marie Curie, Paris 6, France | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina | ||
| 593 | |a Departamento de Matemática, Univ. Tec. Federico S. Maria, Casilla 110-V, Valparaíso, Chile | ||
| 593 | |a Departamento de Matemáticas, Universidade da Coruña, 15071 - A Coruña, Spain | ||
| 593 | |a Comn. Invest. Cie. Provincia B.A., Departamento de Matemática, Universidad Nacional de La Plata, C.C. 172, 1900 - La Plata, Argentina | ||
| 593 | |a GI2MA, Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile | ||
| 690 | 1 | 0 | |a ISOPARAMETRIC QUADRILATERALS |
| 690 | 1 | 0 | |a MITC METHODS |
| 690 | 1 | 0 | |a REISSNER-MINDLIN |
| 690 | 1 | 0 | |a APPROXIMATION THEORY |
| 690 | 1 | 0 | |a BOUNDARY CONDITIONS |
| 690 | 1 | 0 | |a CONVERGENCE OF NUMERICAL METHODS |
| 690 | 1 | 0 | |a FINITE ELEMENT METHOD |
| 690 | 1 | 0 | |a INTEGRATION |
| 690 | 1 | 0 | |a INTERPOLATION |
| 690 | 1 | 0 | |a MATHEMATICAL MODELS |
| 690 | 1 | 0 | |a PERTURBATION TECHNIQUES |
| 690 | 1 | 0 | |a TENSORS |
| 690 | 1 | 0 | |a ERROR ESTIMATION |
| 690 | 1 | 0 | |a ISOPARAMETRIC QUADRILATERALS |
| 690 | 1 | 0 | |a PLATE THICKNESS |
| 690 | 1 | 0 | |a ERROR ANALYSIS |
| 700 | 1 | |a Hernández, E. | |
| 700 | 1 | |a Hervella-Nieto, L. | |
| 700 | 1 | |a Liberman, E. | |
| 700 | 1 | |a Rodríguezh, R. | |
| 773 | 0 | |d Society for Industrial and Applied Mathematics Publications, 2003 |g v. 41 |h pp. 1751-1772 |k n. 5 |p SIAM J Numer Anal |x 00361429 |w (AR-BaUEN)CENRE-263 |t SIAM Journal on Numerical Analysis | |
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| 856 | 4 | 0 | |u https://doi.org/10.1137/S0036142902409410 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_00361429_v41_n5_p1751_Duran |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00361429_v41_n5_p1751_Duran |y Registro en la Biblioteca Digital |
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