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Abstract:

The classical error analysis for Nédélec edge interpolation requires the so-called regularity assumption on the elements. However, in Nicaise (2001, SIAM J. Numer. Anal., 39, 784-816) optimal error estimates were obtained for the lowest order case under the weaker hypothesis of the maximum angle condition. This assumption allows for anisotropic meshes that become useful, for example, for the approximation of solutions with edge singularities. In this paper we prove optimal error estimates for the edge interpolation of any order under the maximum angle condition. We also obtain sharp stability results for that interpolation on appropriate families of elements. mixed finite elements; edge elements; anisotropic finite elements. © 2010 The author.

Registro:

Documento: Artículo
Título:Interpolation error estimates for edge elements on anisotropic meshes
Autor:Lombardi, A.L.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, Los Polvorines, B1613GSX Provincia de Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:anisotropic finite elements; edge elements; mixed finite elements
Año:2011
Volumen:31
Número:4
Página de inicio:1683
Página de fin:1712
DOI: http://dx.doi.org/10.1093/imanum/drq016
Título revista:IMA Journal of Numerical Analysis
Título revista abreviado:IMA J. Numer. Anal.
ISSN:02724979
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v31_n4_p1683_Lombardi

Referencias:

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  • Acosta, G., Apel, T., Durán, R.G., Lombardi, A.L., Error estimates for Raviart-Thomas interpolation of any order on anisotropic tetrahedra (2011) Math. Comput., 80, pp. 147-163
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Citas:

---------- APA ----------
(2011) . Interpolation error estimates for edge elements on anisotropic meshes. IMA Journal of Numerical Analysis, 31(4), 1683-1712.
http://dx.doi.org/10.1093/imanum/drq016
---------- CHICAGO ----------
Lombardi, A.L. "Interpolation error estimates for edge elements on anisotropic meshes" . IMA Journal of Numerical Analysis 31, no. 4 (2011) : 1683-1712.
http://dx.doi.org/10.1093/imanum/drq016
---------- MLA ----------
Lombardi, A.L. "Interpolation error estimates for edge elements on anisotropic meshes" . IMA Journal of Numerical Analysis, vol. 31, no. 4, 2011, pp. 1683-1712.
http://dx.doi.org/10.1093/imanum/drq016
---------- VANCOUVER ----------
Lombardi, A.L. Interpolation error estimates for edge elements on anisotropic meshes. IMA J. Numer. Anal. 2011;31(4):1683-1712.
http://dx.doi.org/10.1093/imanum/drq016