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Abstract:

In this paper we prove error estimates for a piecewise Q1 average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained. © 2005 American Mathematical Society.

Registro:

Documento: Artículo
Título:Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces
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 elements; Weighted norms
Año:2005
Volumen:74
Número:252
Página de inicio:1679
Página de fin:1706
DOI: http://dx.doi.org/10.1090/S0025-5718-05-01732-1
Handle:http://hdl.handle.net/20.500.12110/paper_00255718_v74_n252_p1679_Duran
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00255718_v74_n252_p1679_Duran.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v74_n252_p1679_Duran

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Citas:

---------- APA ----------
Durán, R.G. & Lombardi, A.L. (2005) . Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces. Mathematics of Computation, 74(252), 1679-1706.
http://dx.doi.org/10.1090/S0025-5718-05-01732-1
---------- CHICAGO ----------
Durán, R.G., Lombardi, A.L. "Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces" . Mathematics of Computation 74, no. 252 (2005) : 1679-1706.
http://dx.doi.org/10.1090/S0025-5718-05-01732-1
---------- MLA ----------
Durán, R.G., Lombardi, A.L. "Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces" . Mathematics of Computation, vol. 74, no. 252, 2005, pp. 1679-1706.
http://dx.doi.org/10.1090/S0025-5718-05-01732-1
---------- VANCOUVER ----------
Durán, R.G., Lombardi, A.L. Error estimates on anisotropic Q1 elements for functions in weighted sobolev spaces. Math. Comput. 2005;74(252):1679-1706.
http://dx.doi.org/10.1090/S0025-5718-05-01732-1