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Abstract:

We prove optimal order error estimates for the Raviart-Thomas interpolation of arbitrary order under the maximum angle condition for triangles and under two generalizations of this condition, namely, the so-called three-dimensional maximum angle condition and the regular vertex property, for tetrahedra. Our techniques are different from those used in previous papers on the subject, and the results obtained are more general in several aspects. First, intermediate regularity is allowed; that is, for the Raviart-Thomas interpolation of degree k ≥ 0, we prove error estimates of order j + 1 when the vector field being approximated has components in WJ+1,p, for triangles or tetrahedra, where 0 ≤ j ≤ k and 1 ≤ p ≤ ∞. These results are new even in the two-dimensional case. Indeed, the estimate was known only in the case j = k. On the other hand, in the three-dimensional case, results under the maximum angle condition were known only for k = 0. © 2010 American Mathematical Society.

Registro:

Documento: Artículo
Título:Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra
Autor:Acosta, G.; Apel, T.; Durán, R.G.; Lombardi, A.L.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, Neubiberg, Germany
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, United States
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
Año:2010
Volumen:80
Número:273
Página de inicio:141
Página de fin:163
DOI: http://dx.doi.org/10.1090/S0025-5718-2010-02406-8
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n273_p141_Acosta

Referencias:

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Citas:

---------- APA ----------
Acosta, G., Apel, T., Durán, R.G. & Lombardi, A.L. (2010) . Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra. Mathematics of Computation, 80(273), 141-163.
http://dx.doi.org/10.1090/S0025-5718-2010-02406-8
---------- CHICAGO ----------
Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L. "Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra" . Mathematics of Computation 80, no. 273 (2010) : 141-163.
http://dx.doi.org/10.1090/S0025-5718-2010-02406-8
---------- MLA ----------
Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L. "Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra" . Mathematics of Computation, vol. 80, no. 273, 2010, pp. 141-163.
http://dx.doi.org/10.1090/S0025-5718-2010-02406-8
---------- VANCOUVER ----------
Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L. Error estimates for raviart-thomas interpolation of any order on anisotropic tetrahedra. Math. Comput. 2010;80(273):141-163.
http://dx.doi.org/10.1090/S0025-5718-2010-02406-8