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.
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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