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
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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
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Palabras clave: | Anisotropic finite elements; Mixed finite elements; Raviart-thomas |
Año: | 2010
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Volumen: | 80
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Número: | 273
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Página de inicio: | 141
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Página de fin: | 163
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DOI: |
http://dx.doi.org/10.1090/S0025-5718-2010-02406-8 |
Título revista: | Mathematics of Computation
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Título revista abreviado: | Math. Comput.
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ISSN: | 00255718
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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