Artículo
Durán, R.G.; Lombardi, A.L. "Error estimates for the Raviart-Thomas interpolation under the maximum angle condition" (2008) SIAM Journal on Numerical Analysis. 46(3):1442-1453
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Abstract:
The classical error analysis for the Raviart-Thomas interpolation on triangular elements requires the so-called regularity of the elements, or equivalently, the minimum angle condition. However, in the lowest order case, optimal order error estimates have been obtained in [G. Acosta and R. G. Durán, SIAM J. Nurner. Anal., 37 (2000), pp. 18-36] replacing the regularity hypothesis by the maximum angle condition, which was known to be sufficient to prove estimates for the standard Lagrange interpolation. In this paper we prove error estimates on triangular elements for the Raviart-Thomas interpolation of any order under the maximum angle condition. Also, we show how our arguments can be extended to the three-dimensional case to obtain error estimates for tetrahedral elements under the regular vertex property introduced in [G. Acosta and R. G. Durán, SIAM J. Numer. Anal., 37 (2000), pp. 18-36] © 2008 Society for Industrial and Applied Mathematics.
Registro:
| Documento: | Artículo |
| Título: | Error estimates for the Raviart-Thomas interpolation under the maximum angle condition |
| Autor: | Durán, R.G.; Lombardi, A.L. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina |
| Palabras clave: | Anisotropic finite elements; Mixed finite elements; Raviart-Thomas; Computational mechanics; Error analysis; Three dimensional; Anisotropic finite elements; Error estimates; Lagrange interpolations; Maximum angle conditions; Mixed finite elements; Raviart-Thomas; Tetrahedral elements; Triangular elements; Interpolation |
| Año: | 2008 |
| Volumen: | 46 |
| Número: | 3 |
| Página de inicio: | 1442 |
| Página de fin: | 1453 |
| DOI: | http://dx.doi.org/10.1137/060665312 |
| 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_v46_n3_p1442_Duran |
Referencias:
- ACOSTA, G., DURÁN, R.G., The maximum angle condition for mixed and nonconforming elements: Application to the Stokes equations (2000) SIAM J. Numer. Anal, 37, pp. 18-36
- T. APEL, Anisotropic Finite Elements: Local Estimates and Applications, Adv. Numer. Math., Teubner, Stuttgart, 1999; BABUSKA, I., AZIZ, A.K., On the angle condition in the finite element method (1976) SIAM J. Numer. Anal, 13, pp. 214-226
- BRENNER, S., SCOTT, L.R., (1994) The Mathematical Theory of Finite Element Methods, , Springer, New York
- CIARLET, P.G., (1978) The Finite Element Method for Elliptic Problems, , North-Holland, Amsterdam
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- DURÁN, R.G., Error estimates for anisotropic finite elements and applications (2006) Proceedings of the International Congress of Mathematicians
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- KRÍZEK, M., On the maximum angle condition for linear tetrahedral elements (1992) SIAM J. Numer. Anal, 29, pp. 513-520
- NEDELEC, J.C., Mixed finite elements in &Rdbl;3 (1980) Numer. Math, 35, pp. 315-341
- RAVIART, P.A., THOMAS, J.M., A mixed finite element method for second order elliptic problems (1977) Lecture Notes in Math, 606, pp. 292-315. , Mathematical Aspects of the Finite Element Method, I. Galligani and E. Magenes, eds, Springer, Berlin
- AL SHENK, N., Uniform error estimates for certain narrow Lagrange finite elements (1994) Math. Comp, 63, pp. 105-119
- THOMAS, J.M., (1977) Sur l'Analyse Numérique des Méthodes d'Éléments Finis Hybrides et Mixtes, , Thèse d'Etat, Université Pierre et Marie Curie, Paris
Citas:
---------- APA ----------
Durán, R.G. & Lombardi, A.L. (2008) . Error estimates for the Raviart-Thomas interpolation under the maximum angle condition. SIAM Journal on Numerical Analysis, 46(3), 1442-1453.http://dx.doi.org/10.1137/060665312
---------- CHICAGO ----------
Durán, R.G., Lombardi, A.L. "Error estimates for the Raviart-Thomas interpolation under the maximum angle condition" . SIAM Journal on Numerical Analysis 46, no. 3 (2008) : 1442-1453.http://dx.doi.org/10.1137/060665312
---------- MLA ----------
Durán, R.G., Lombardi, A.L. "Error estimates for the Raviart-Thomas interpolation under the maximum angle condition" . SIAM Journal on Numerical Analysis, vol. 46, no. 3, 2008, pp. 1442-1453.http://dx.doi.org/10.1137/060665312
---------- VANCOUVER ----------
Durán, R.G., Lombardi, A.L. Error estimates for the Raviart-Thomas interpolation under the maximum angle condition. SIAM J Numer Anal. 2008;46(3):1442-1453.http://dx.doi.org/10.1137/060665312
