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Abstract:

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.

Registro:

Documento: Artículo
Título:A posteriori error estimates for the finite element approximation of eigenvalue problems
Autor:Duran, R.G.; Padra, C.; Rodríguez, R.
Filiación:Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Centra Atómico Bariloche, 8400 Bariloche, Río Negro, Argentina
GI2M A, Depto. de Ing. Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
CONICET, Buenos Aires, Argentina
Palabras clave:A posteriori error estimates; Eigenvalue problems; Finite elements
Año:2003
Volumen:13
Número:8
Página de inicio:1219
Página de fin:1229
DOI: http://dx.doi.org/10.1142/S0218202503002878
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_v13_n8_p1219_Duran

Referencias:

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  • Strang, G., Fix, G.J., (1973) An Analysis of the Finite Element Method, , Prentice Hall
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Citas:

---------- APA ----------
Duran, R.G., Padra, C. & Rodríguez, R. (2003) . A posteriori error estimates for the finite element approximation of eigenvalue problems. Mathematical Models and Methods in Applied Sciences, 13(8), 1219-1229.
http://dx.doi.org/10.1142/S0218202503002878
---------- CHICAGO ----------
Duran, R.G., Padra, C., Rodríguez, R. "A posteriori error estimates for the finite element approximation of eigenvalue problems" . Mathematical Models and Methods in Applied Sciences 13, no. 8 (2003) : 1219-1229.
http://dx.doi.org/10.1142/S0218202503002878
---------- MLA ----------
Duran, R.G., Padra, C., Rodríguez, R. "A posteriori error estimates for the finite element approximation of eigenvalue problems" . Mathematical Models and Methods in Applied Sciences, vol. 13, no. 8, 2003, pp. 1219-1229.
http://dx.doi.org/10.1142/S0218202503002878
---------- VANCOUVER ----------
Duran, R.G., Padra, C., Rodríguez, R. A posteriori error estimates for the finite element approximation of eigenvalue problems. Math. Models Methods Appl. Sci. 2003;13(8):1219-1229.
http://dx.doi.org/10.1142/S0218202503002878