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Abstract:

We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom. © 2012 IMACS. Published by Elsevier B.V. All rights reserved.

Registro:

Documento: Artículo
Título:A posteriori error estimates for non-conforming approximation of eigenvalue problems
Autor:Dari, E.A.; Durán, R.G.; Padra, C.
Filiación:Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, CONICET, R8402AGP Bariloche, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, 1428 Buenos Aires, Argentina
Palabras clave:A posteriori error estimators; Eigenvalue problems; Non-conforming finite elements; A-posteriori error estimates; Adaptive procedure; Eigen-value; Eigenvalue problem; Eigenvalues; Energy norm; Error estimators; Higher order terms; Laplacians; Non-conforming finite elements; Nonconforming finite element; Number of degrees of freedom; Numerical example; Posteriori error estimator; Three dimensions; Upper Bound; Error analysis; Switching systems; Eigenvalues and eigenfunctions
Año:2012
Volumen:62
Número:5
Página de inicio:580
Página de fin:591
DOI: http://dx.doi.org/10.1016/j.apnum.2012.01.005
Título revista:Applied Numerical Mathematics
Título revista abreviado:Appl Numer Math
ISSN:01689274
CODEN:ANMAE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v62_n5_p580_Dari

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Citas:

---------- APA ----------
Dari, E.A., Durán, R.G. & Padra, C. (2012) . A posteriori error estimates for non-conforming approximation of eigenvalue problems. Applied Numerical Mathematics, 62(5), 580-591.
http://dx.doi.org/10.1016/j.apnum.2012.01.005
---------- CHICAGO ----------
Dari, E.A., Durán, R.G., Padra, C. "A posteriori error estimates for non-conforming approximation of eigenvalue problems" . Applied Numerical Mathematics 62, no. 5 (2012) : 580-591.
http://dx.doi.org/10.1016/j.apnum.2012.01.005
---------- MLA ----------
Dari, E.A., Durán, R.G., Padra, C. "A posteriori error estimates for non-conforming approximation of eigenvalue problems" . Applied Numerical Mathematics, vol. 62, no. 5, 2012, pp. 580-591.
http://dx.doi.org/10.1016/j.apnum.2012.01.005
---------- VANCOUVER ----------
Dari, E.A., Durán, R.G., Padra, C. A posteriori error estimates for non-conforming approximation of eigenvalue problems. Appl Numer Math. 2012;62(5):580-591.
http://dx.doi.org/10.1016/j.apnum.2012.01.005