Abstract:
In this paper, we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, and C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix–Raviart nonconforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.
Registro:
Documento: |
Artículo
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Título: | A posteriori error analysis for nonconforming approximation of multiple eigenvalues |
Autor: | Boffi, D.; Durán, R.G.; Gardini, F.; Gastaldi, L. |
Filiación: | Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, Pavia, Italy Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Buenos Aires, 1428, Argentina DICATAM Sez. di Matematica, Università di Brescia, Brescia, Italy
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Palabras clave: | a posteriori error analysis; eigenvalue problems; nonconforming finite elements; Adaptive algorithms; Error analysis; Finite element method; Switching systems; Eigenvalue problem; Eigenvalues; Multiple eigenvalues; Nonconforming finite element; Posteriori error analysis; Posteriori error indicator; Eigenvalues and eigenfunctions |
Año: | 2017
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Volumen: | 40
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Número: | 2
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Página de inicio: | 350
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Página de fin: | 369
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DOI: |
http://dx.doi.org/10.1002/mma.3452 |
Título revista: | Mathematical Methods in the Applied Sciences
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Título revista abreviado: | Math Methods Appl Sci
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ISSN: | 01704214
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CODEN: | MMSCD
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01704214_v40_n2_p350_Boffi |
Referencias:
- Crouzeix, M., Raviart, P.-A., Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I (1973) Revue Française d'Automatique Informatique Recherche Opérationnelle Analyse Numérique, 7 (R-3), pp. 33-75
- Boffi, D., Finite element approximation of eigenvalue problems (2010) Acta Numerica, 19, pp. 1-120
- Dari, E., Durán, R.G., Padra, C., A posteriori error estimates for non conforming approximation of eigenvalue problems (2012) Applied Numerical Mathematics, 62, pp. 580-591
- Bank, R.E., Grubišić, L., Ovall, J.S., A framework for robust eigenvalue and eigenvector error estimation and Ritz value convergence enhancement (2013) Applied Numerical Mathematics, 66, pp. 1-29
- Dai, X., He, L., Zhou, A., Convergence rate and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues (2014) IMA Journal of Numerical Analysis
- Gallistl, D., An optimal adaptive FEM for eigenvalue clusters (2014) Numerische Mathematik
- Grubišić, L., Ovall, J.S., On estimators for eigenvalue/eigenvector approximations (2009) Mathematics of Computation, 78 (266), pp. 739-770
- Solin, P., Giani, S., An iterative adaptive finite element method for elliptic eigenvalue problems (2012) Journal of Computational and Applied Mathematics, 236, pp. 4582-4599
- Knyazev, A.V., New estimates for Ritz vectors (1997) Mathematics of Computation, 66 (219), pp. 985-995
- Armentano, M.G., Durán, R.G., Asymptotic lower bounds for eigenvalues by nonconforming finite element methods (2004) Electronic Transactions on Numerical Analysis, 17, pp. 93-101. , (electronic)
- Carstensen, C., Gedicke, J., Guaranteed lower bounds for eigenvalues (2014) Mathematics of Computation, 83 (290), pp. 2605-2629
- Gastaldi, L., Nochetto, R., Optimal L∞-error estimates for nonconforming and mixed element methods of lowest order (1987) Numerische Mathematik, 50, pp. 587-611
- Knyazev, A.V., Osborn, J.E., New a priori FEM error estimates for eigenvalues (2006) SIAM Journal on Numerical Analysis, 43 (6), pp. 2647-2667
- Kato, T., (1995) Perturbation theory for linear operators, , Springer-Verlag, New York
- Dörfler, W., A convergent adaptive algorithm for Poisson's equation (1996) SIAM Journal on Numerical Analysis, 33, pp. 1106-1124
Citas:
---------- APA ----------
Boffi, D., Durán, R.G., Gardini, F. & Gastaldi, L.
(2017)
. A posteriori error analysis for nonconforming approximation of multiple eigenvalues. Mathematical Methods in the Applied Sciences, 40(2), 350-369.
http://dx.doi.org/10.1002/mma.3452---------- CHICAGO ----------
Boffi, D., Durán, R.G., Gardini, F., Gastaldi, L.
"A posteriori error analysis for nonconforming approximation of multiple eigenvalues"
. Mathematical Methods in the Applied Sciences 40, no. 2
(2017) : 350-369.
http://dx.doi.org/10.1002/mma.3452---------- MLA ----------
Boffi, D., Durán, R.G., Gardini, F., Gastaldi, L.
"A posteriori error analysis for nonconforming approximation of multiple eigenvalues"
. Mathematical Methods in the Applied Sciences, vol. 40, no. 2, 2017, pp. 350-369.
http://dx.doi.org/10.1002/mma.3452---------- VANCOUVER ----------
Boffi, D., Durán, R.G., Gardini, F., Gastaldi, L. A posteriori error analysis for nonconforming approximation of multiple eigenvalues. Math Methods Appl Sci. 2017;40(2):350-369.
http://dx.doi.org/10.1002/mma.3452