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Abstract:

In this paper we analyse piecewise linear finite element approximations of the Laplace eigenvalue problem in the plane domain Ω = (x,y): 0 < x < 1, 0 < y < x, which gives for 1< the simplest model of an external cusp. Since Ω is curved and non-Lipschitz, the classical spectral theory cannot be applied directly. We present the eigenvalue problem in a proper setting, and relying on known convergence results for the associated source problem with <3, we obtain a quasi-optimal order of convergence for the eigenpairs. © 2013 The authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Registro:

Documento: Artículo
Título:Eigenvalue problems in a non-Lipschitz domain
Autor:Acosta, G.; Armentano, M.G.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, IMAS-CONICET, 1428 Buenos Aires, Argentina
Idioma: Inglés
Palabras clave:cuspidal domains; eigenvalue problems; finite elements; graded meshes
Año:2014
Volumen:34
Número:1
Página de inicio:83
Página de fin:95
DOI: http://dx.doi.org/10.1093/imanum/drt012
Título revista:IMA Journal of Numerical Analysis
Título revista abreviado:IMA J. Numer. Anal.
ISSN:02724979
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_02724979_v34_n1_p83_Acosta

Referencias:

  • Acosta, G., Armentano, M.G., Finite element approximations in a non-Lipschitz domain: Part. II (2011) Math. Comp., 80, pp. 1949-1978
  • Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L., Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp (2005) J. Math. Anal. Appl., 310, pp. 397-411
  • Acosta, G., Armentano, M.G., Durán, R.G., Lombardi, A.L., Finite element approximations in a non-Lipschitz domain (2007) SIAM J. Numer. Anal., 45, pp. 277-295
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Citas:

---------- APA ----------
Acosta, G. & Armentano, M.G. (2014) . Eigenvalue problems in a non-Lipschitz domain. IMA Journal of Numerical Analysis, 34(1), 83-95.
http://dx.doi.org/10.1093/imanum/drt012
---------- CHICAGO ----------
Acosta, G., Armentano, M.G. "Eigenvalue problems in a non-Lipschitz domain" . IMA Journal of Numerical Analysis 34, no. 1 (2014) : 83-95.
http://dx.doi.org/10.1093/imanum/drt012
---------- MLA ----------
Acosta, G., Armentano, M.G. "Eigenvalue problems in a non-Lipschitz domain" . IMA Journal of Numerical Analysis, vol. 34, no. 1, 2014, pp. 83-95.
http://dx.doi.org/10.1093/imanum/drt012
---------- VANCOUVER ----------
Acosta, G., Armentano, M.G. Eigenvalue problems in a non-Lipschitz domain. IMA J. Numer. Anal. 2014;34(1):83-95.
http://dx.doi.org/10.1093/imanum/drt012