A posteriori error analysis for nonconforming approximation of multiple eigenvalues

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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...

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Autor principal: Boffi, D.
Otros Autores: Durán, R.G, Gardini, F., Gastaldi, L.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: John Wiley and Sons Ltd 2017
Acceso en línea:Registro en Scopus
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100 1 |a Boffi, D. 
245 1 2 |a A posteriori error analysis for nonconforming approximation of multiple eigenvalues 
260 |b John Wiley and Sons Ltd  |c 2017 
270 1 0 |m Boffi, D.; Dipartimento di Matematica ‘F. Casorati’, Università di PaviaItaly; email: daniele.boffi@unipv.it 
506 |2 openaire  |e Política editorial 
504 |a 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 
504 |a Boffi, D., Finite element approximation of eigenvalue problems (2010) Acta Numerica, 19, pp. 1-120 
504 |a 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 
504 |a 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 
504 |a 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 
504 |a Gallistl, D., An optimal adaptive FEM for eigenvalue clusters (2014) Numerische Mathematik 
504 |a Grubišić, L., Ovall, J.S., On estimators for eigenvalue/eigenvector approximations (2009) Mathematics of Computation, 78 (266), pp. 739-770 
504 |a 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 
504 |a Knyazev, A.V., New estimates for Ritz vectors (1997) Mathematics of Computation, 66 (219), pp. 985-995 
504 |a 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) 
504 |a Carstensen, C., Gedicke, J., Guaranteed lower bounds for eigenvalues (2014) Mathematics of Computation, 83 (290), pp. 2605-2629 
504 |a Gastaldi, L., Nochetto, R., Optimal L∞-error estimates for nonconforming and mixed element methods of lowest order (1987) Numerische Mathematik, 50, pp. 587-611 
504 |a 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 
504 |a Kato, T., (1995) Perturbation theory for linear operators, , Springer-Verlag, New York 
504 |a Dörfler, W., A convergent adaptive algorithm for Poisson's equation (1996) SIAM Journal on Numerical Analysis, 33, pp. 1106-1124 
520 3 |a 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.  |l eng 
593 |a Dipartimento di Matematica ‘F. Casorati’, Università di Pavia, Pavia, Italy 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Buenos Aires, 1428, Argentina 
593 |a DICATAM Sez. di Matematica, Università di Brescia, Brescia, Italy 
690 1 0 |a A POSTERIORI ERROR ANALYSIS 
690 1 0 |a EIGENVALUE PROBLEMS 
690 1 0 |a NONCONFORMING FINITE ELEMENTS 
690 1 0 |a ADAPTIVE ALGORITHMS 
690 1 0 |a ERROR ANALYSIS 
690 1 0 |a FINITE ELEMENT METHOD 
690 1 0 |a SWITCHING SYSTEMS 
690 1 0 |a EIGENVALUE PROBLEM 
690 1 0 |a EIGENVALUES 
690 1 0 |a MULTIPLE EIGENVALUES 
690 1 0 |a NONCONFORMING FINITE ELEMENT 
690 1 0 |a POSTERIORI ERROR ANALYSIS 
690 1 0 |a POSTERIORI ERROR INDICATOR 
690 1 0 |a EIGENVALUES AND EIGENFUNCTIONS 
700 1 |a Durán, R.G. 
700 1 |a Gardini, F. 
700 1 |a Gastaldi, L. 
773 0 |d John Wiley and Sons Ltd, 2017  |g v. 40  |h pp. 350-369  |k n. 2  |p Math Methods Appl Sci  |x 01704214  |t Mathematical Methods in the Applied Sciences 
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856 4 0 |u https://doi.org/10.1002/mma.3452  |y DOI 
856 4 0 |u https://hdl.handle.net/20.500.12110/paper_01704214_v40_n2_p350_Boffi  |y Handle 
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999 |c 76219 

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