A posteriori error estimates for the finite element approximation of eigenvalue problems

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This paper deals with a posteriori error estimators for the linear finite element approximation of second-order elliptic eigenvalue problems in two or three dimensions. First, we give a simple proof of the equivalence, up to higher order terms, between the error and a residual type error estimator....

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Detalles Bibliográficos
Autor principal: Duran, R.G
Otros Autores: Padra, C., Rodríguez, R.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: 2003
Acceso en línea:Registro en Scopus
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Biblioteca Central Dr. Luis F. Leloir (FCEN) de Universidad de Buenos Aires
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100 1 |a Duran, R.G. 
245 1 2 |a A posteriori error estimates for the finite element approximation of eigenvalue problems 
260 |c 2003 
270 1 0 |m Duran, R.G.; Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina; email: rduran@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Ainsworth, M., Oden, J.T., (2000) A Posteriori Error Estimation in Finite Element Analysis, , Wiley 
504 |a Arnold, D.N., Mukherjee, A., Pouly, L., Locally adapted tetrahedral meshes using bisection (2000) SIAM J. Sci. Comput., 22, pp. 431-448 
504 |a Babuška, I., Miller, A., A feedback finite element method with a posteriori error estimation. Part I: The finite element method and some basic properties of the a posteriori error estimator (1987) Comp. Methods Appl. Mech. Engrg., 81, pp. 1-40 
504 |a Babus̈ka, I., Osborn, J., Eigenvalue Problems (1991) Handbook of Numerical Analysis, 2, pp. 641-787. , eds. P. G. Ciarlet and J. L. Lions (North-Holland) 
504 |a Carstensen, C., Verfürth, R., Edge residuals dominate a posteriori error estimates for low order finite element methods (1999) SIAM J. Numer. Anal., 36, pp. 1571-1587 
504 |a Clément, P., Approximation by finite element functions using local regularization (1975) RAIRO, R-2, pp. 77-84 
504 |a Larson, M.G., A posteriori and a priori error analysis for finite element approximations of self-adjoint elliptic eigenvalue problems (2000) SIAM J. Numer. Anal., 38, pp. 608-625 
504 |a Nochetto, R., Pointwise a posteriori error estimates for elliptic problems on highly graded meshes (1995) Math. Comput., 84, pp. 1-22 
504 |a Raviart, P.A., Thomas, J.M., (1983) Introduction à l'Analyse Numérique des Equations aux Dérivées Partielles, , Masson 
504 |a Rivara, M.C., Mesh refinement processes based on the generalized bisection of simplices (1984) SIAM J. Numer. Anal., 21, pp. 604-613 
504 |a Rivara, M.C., Vénere, M.J., Cost analysis of the longest-side refinement algorithm for triangulations (1996) Eng. Comput., 12, pp. 224-234 
504 |a Rodríguez, R., Some remarks on Zienkiewicz-Zhu estimator (1994) Numer. Methods Partial Differential Equations, 10, pp. 625-635 
504 |a Strang, G., Fix, G.J., (1973) An Analysis of the Finite Element Method, , Prentice Hall 
504 |a Verfürth, R., (1996) A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, , Wiley & Teubner 
504 |a Verfürth, R., A posteriori error estimates for nonlinear problems (1989) Math. Comput., 62, pp. 445-475 
520 3 |a This paper deals with a posteriori error estimators for the linear finite element approximation of second-order elliptic eigenvalue problems in two or three dimensions. First, we give a simple proof of the equivalence, up to higher order terms, between the error and a residual type error estimator. Second, we prove that the volumetric part of the residual is dominated by a constant times the edge or face residuals, again up to higher order terms. This result was not known for eigenvalue problems.  |l eng 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PICT 03-05009 
536 |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PICT 12-03239, PIP 0660/98 
536 |a Detalles de la financiación: Ricardo G. Durán was partially supported by ANPCyT under grant PICT 03-05009 and by CONICET under grant PIP 0660/98. Claudio Padra was partially supported by ANPCyT under grant PICT 12-03239. Claudio Padra and Rodolfo Rodríguez were partially supported by FONDAP in Applied Mathematics. 
593 |a Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina 
593 |a Centra Atómico Bariloche, 8400 Bariloche, Río Negro, Argentina 
593 |a GI2M A, Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile 
593 |a CONICET, Buenos Aires, Argentina 
690 1 0 |a A POSTERIORI ERROR ESTIMATES 
690 1 0 |a EIGENVALUE PROBLEMS 
690 1 0 |a FINITE ELEMENTS 
700 1 |a Padra, C. 
700 1 |a Rodríguez, R. 
773 0 |d 2003  |g v. 13  |h pp. 1219-1229  |k n. 8  |p Math. Models Methods Appl. Sci.  |x 02182025  |w (AR-BaUEN)CENRE-6043  |t Mathematical Models and Methods in Applied Sciences 
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856 4 0 |u https://doi.org/10.1142/S0218202503002878  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_02182025_v13_n8_p1219_Duran  |y Handle 
856 4 0 |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v13_n8_p1219_Duran  |y Registro en la Biblioteca Digital 
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962 |a info:eu-repo/semantics/article  |a info:ar-repo/semantics/artículo  |b info:eu-repo/semantics/publishedVersion 
999 |c 65833 

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