Artículo

Boffi, D.; Durán, R.G.; Gardini, F.; Gastaldi, L."A posteriori error analysis for nonconforming approximation of multiple eigenvalues" (2017) Mathematical Methods in the Applied Sciences. 40(2):350-369
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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
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
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
Volumen:40
Número:2
Página de inicio:350
Página de fin:369
DOI: http://dx.doi.org/10.1002/mma.3452
Handle:http://hdl.handle.net/20.500.12110/paper_01704214_v40_n2_p350_Boffi
Título revista:Mathematical Methods in the Applied Sciences
Título revista abreviado:Math Methods Appl Sci
ISSN:01704214
CODEN:MMSCD
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
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  • 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
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  • Grubišić, L., Ovall, J.S., On estimators for eigenvalue/eigenvector approximations (2009) Mathematics of Computation, 78 (266), pp. 739-770
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  • 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
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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