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Abstract:

In a paper by R. Durán, A. Lombardi, and the authors (2007) the finite element method was applied to a non-homogeneous Neumann problem on a cuspidal domain Ω ⊂R{double struck}2, and quasi-optimal order error estimates in the energy norm were obtained for certain graded meshes. In this paper, we study the error in the L2 norm obtaining similar results by using graded meshes of the type considered in that paper. Since many classical results in the theory Sobolev spaces do not apply to the domain under consideration, our estimates require a particular duality treatment working on appropriate weighted spaces. On the other hand, since the discrete domain Ωh verifies Ω ⊂ Ωh, in the above-mentioned paper the source term of the Poisson problem was taken equal to 0 outside Ω in the variational discrete formulation. In this article we also consider the case in which this condition does not hold and obtain more general estimates, which can be useful in different problems, for instance in the study of the effect of numerical integration, or in eigenvalue approximations. © 2011 American Mathematical Society.

Registro:

Documento: Artículo
Título:Finite element approximations in a non-Lipschitz domain: Part II
Autor:Acosta, G.; Armentano, M.G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Cuspidal domains; Finite elements; Graded meshes
Año:2011
Volumen:80
Número:276
Página de inicio:1949
Página de fin:1978
DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02481-6
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00255718_v80_n276_p1949_Acosta.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v80_n276_p1949_Acosta

Referencias:

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Citas:

---------- APA ----------
Acosta, G. & Armentano, M.G. (2011) . Finite element approximations in a non-Lipschitz domain: Part II. Mathematics of Computation, 80(276), 1949-1978.
http://dx.doi.org/10.1090/S0025-5718-2011-02481-6
---------- CHICAGO ----------
Acosta, G., Armentano, M.G. "Finite element approximations in a non-Lipschitz domain: Part II" . Mathematics of Computation 80, no. 276 (2011) : 1949-1978.
http://dx.doi.org/10.1090/S0025-5718-2011-02481-6
---------- MLA ----------
Acosta, G., Armentano, M.G. "Finite element approximations in a non-Lipschitz domain: Part II" . Mathematics of Computation, vol. 80, no. 276, 2011, pp. 1949-1978.
http://dx.doi.org/10.1090/S0025-5718-2011-02481-6
---------- VANCOUVER ----------
Acosta, G., Armentano, M.G. Finite element approximations in a non-Lipschitz domain: Part II. Math. Comput. 2011;80(276):1949-1978.
http://dx.doi.org/10.1090/S0025-5718-2011-02481-6