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Abstract:

In this paper we introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart-Thomas of the lowest order. We define an error estimator of the residual type which can be computed locally from the approximate eigenvector and prove that the estimator is equivalent to the norm of the error in the approximation of the eigenvector up to higher order terms. The constants involved in this equivalence depend on the corresponding eigenvalue but are independent of the mesh size, provided the meshes satisfy the usual minimum angle condition. Moreover, the square root of the error in the approximation of the eigenvalue is also bounded by a constant times the estimator.

Registro:

Documento: Artículo
Título:A posteriori error estimators for mixed approximations of eigenvalue problems
Autor:Durán, R.G.; Gastaldi, L.; Padra, C.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
Dipartimento di Matematica, Univ. di Roma La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
Centro Atómico Bariloche, 8400, Bariloche, Rio Negro, Argentina
Año:1999
Volumen:9
Número:8
Página de inicio:1165
Página de fin:1178
DOI: http://dx.doi.org/10.1142/S021820259900052X
Título revista:Mathematical Models and Methods in Applied Sciences
Título revista abreviado:Math. Models Methods Appl. Sci.
ISSN:02182025
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v9_n8_p1165_Duran

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Citas:

---------- APA ----------
Durán, R.G., Gastaldi, L. & Padra, C. (1999) . A posteriori error estimators for mixed approximations of eigenvalue problems. Mathematical Models and Methods in Applied Sciences, 9(8), 1165-1178.
http://dx.doi.org/10.1142/S021820259900052X
---------- CHICAGO ----------
Durán, R.G., Gastaldi, L., Padra, C. "A posteriori error estimators for mixed approximations of eigenvalue problems" . Mathematical Models and Methods in Applied Sciences 9, no. 8 (1999) : 1165-1178.
http://dx.doi.org/10.1142/S021820259900052X
---------- MLA ----------
Durán, R.G., Gastaldi, L., Padra, C. "A posteriori error estimators for mixed approximations of eigenvalue problems" . Mathematical Models and Methods in Applied Sciences, vol. 9, no. 8, 1999, pp. 1165-1178.
http://dx.doi.org/10.1142/S021820259900052X
---------- VANCOUVER ----------
Durán, R.G., Gastaldi, L., Padra, C. A posteriori error estimators for mixed approximations of eigenvalue problems. Math. Models Methods Appl. Sci. 1999;9(8):1165-1178.
http://dx.doi.org/10.1142/S021820259900052X