A posteriori error estimates for non-conforming approximation of eigenvalue problems
We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the err...
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2012
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| LEADER | 06996caa a22008417a 4500 | ||
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| 001 | PAPER-9656 | ||
| 003 | AR-BaUEN | ||
| 005 | 20230518203936.0 | ||
| 008 | 190411s2012 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84857921993 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 030 | |a ANMAE | ||
| 100 | 1 | |a Dari, E.A. | |
| 245 | 1 | 2 | |a A posteriori error estimates for non-conforming approximation of eigenvalue problems |
| 260 | |c 2012 | ||
| 270 | 1 | 0 | |m Padra, C.; Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, CONICET, R8402AGP Bariloche, Argentina; email: padra@cab.cnea.gov.ar |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Acosta, G., Durán, R.G., Error estimator for a mixed method (1996) Numer. Math., 74, pp. 385-395 | ||
| 504 | |a Ainsworth, M., Robust a posteriori error estimation for nonconforming finite element approximation (2005) SIAM Journal on Numerical Analysis, 42 (6), pp. 2320-2341. , DOI 10.1137/S0036142903425112 | ||
| 504 | |a Alonso, A., Error estimator for a mixed method (1996) Numer. Math., 74, pp. 385-395 | ||
| 504 | |a Armentano, M.G., Duran, R.G., Asymptotic lower bounds for eigenvalues by nonconforming finite element methods (2004) Electronic Transactions on Numerical Analysis, 17, pp. 93-101. , http://etna.mcs.kent.edu/vol.17.2004/pp93-101.dir/pp93-101.pdf | ||
| 504 | |a Arnold, D.N., Brezzi, F., Mixed and nonconforming finite element methods implementation, postprocessing and error estimates (1985) R.A.I.R.O., Modél. Math. Anal. Numer., 19, pp. 7-32 | ||
| 504 | |a Boffi, D., Brezzi, F., Demkowicz, L.F., Durán, R.G., Falk, R.S., Fortin, M., Finite elements, compatibility conditions, and applications (1939) Lecture Notes in Mathematics, , D. Boffi, Lucia Gastaldi, Springer-Verlag Berlin | ||
| 504 | |a Bogdan, K., Sharp estimates for the green function in Lipschitz domains (2000) J. Math. Anal. Appl., 243, pp. 326-337 | ||
| 504 | |a Carstensen, C., A posteriori error estimate for the mixed finite element method (1997) Math. Comp., 66, pp. 465-476 | ||
| 504 | |a Crouzeix, M., Raviart, P.A., Conforming and non-conforming finite element methods for solving the stationary Stokes equations (1973) R.A.I.R.O. Anal. Numer., 7, pp. 33-76 | ||
| 504 | |a Dari, E., Durán, R.G., Padra, C., Vampa, V., A posteriori error estimators for nonconforming finite element methods (1996) Math. Model. Numer. Anal., 30, pp. 385-400 | ||
| 504 | |a Dauge, M., Problémes de Neumann et de Dirichlet sur un polyédre dans R 3: Regularité dans des espaces de Sobolev Lp (1988) C. R. Acad. Sci. Paris i, 307, pp. 27-32 | ||
| 504 | |a Durán, R.G., Padra, C., An error estimator for nonconforming approximations of a nonlinear problem (1994) Finite Element Methods, Fifty Years of the Courant Element, pp. 201-205. , M. Krizek, P. Neittaanmaki, R. Stenberg, Marcel Dekker | ||
| 504 | |a Marini, L.D., An inexpensive method for the evaluation of the solution of the lowest order Raviart-Thomas mixed method (1985) SIAM J. Numer. Anal., 22, pp. 493-496 | ||
| 504 | |a Raviart, P.A., Thomas, J.M., (1983) Introduction À LAnalyse Numérique des Equations Aux Dérivées Partielles, , Masson | ||
| 504 | |a Rivara, M.C., Algorithms for refining triangular grid suitable for adaptive and multigrid techniques (1984) International Journal for Numerical Methods in Engineering, 20 (4), pp. 745-756 | ||
| 504 | |a Rivara, M.C., Mesh refinement processes based on the generalized bisection of simplices (1984) SIAM J. Numer. Anal., 21, pp. 604-613 | ||
| 520 | 3 | |a We consider the approximation of eigenvalue problem for the Laplacian by the Crouzeix-Raviart non-conforming finite elements in two and three dimensions. Extending known techniques for source problems, we introduce a posteriori error estimators for eigenvectors and eigenvalues. We prove that the error estimator is equivalent to the energy norm of the eigenvector error up to higher order terms. Moreover, we prove that our estimator provides an upper bound for the error in the approximation of the first eigenvalue, also up to higher order terms. We present numerical examples of an adaptive procedure based on our error estimator in two and three dimensions. These examples show that the error in the adaptive procedure is optimal in terms of the number of degrees of freedom. © 2012 IMACS. Published by Elsevier B.V. All rights reserved. |l eng | |
| 536 | |a Detalles de la financiación: Universidad de Buenos Aires, X070 | ||
| 536 | |a Detalles de la financiación: Universidad Nacional de Cuyo, 06-C319, 06-C287 | ||
| 536 | |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, PICT 01307 | ||
| 536 | |a Detalles de la financiación: Consejo Nacional de Investigaciones Científicas y Técnicas, PIP 11220090100625 | ||
| 536 | |a Detalles de la financiación: This research was supported by ANPCyT (grant PICT 01307), by Universidad de Buenos Aires (grant X070), by CONICET (grant PIP 11220090100625) and by Universidad Nacional de Cuyo (grants 06-C287 and 06-C319). | ||
| 593 | |a Centro Atómico Bariloche, Comisión Nacional de Energía Atómica, CONICET, R8402AGP Bariloche, Argentina | ||
| 593 | |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a A POSTERIORI ERROR ESTIMATORS |
| 690 | 1 | 0 | |a EIGENVALUE PROBLEMS |
| 690 | 1 | 0 | |a NON-CONFORMING FINITE ELEMENTS |
| 690 | 1 | 0 | |a A-POSTERIORI ERROR ESTIMATES |
| 690 | 1 | 0 | |a ADAPTIVE PROCEDURE |
| 690 | 1 | 0 | |a EIGEN-VALUE |
| 690 | 1 | 0 | |a EIGENVALUE PROBLEM |
| 690 | 1 | 0 | |a EIGENVALUES |
| 690 | 1 | 0 | |a ENERGY NORM |
| 690 | 1 | 0 | |a ERROR ESTIMATORS |
| 690 | 1 | 0 | |a HIGHER ORDER TERMS |
| 690 | 1 | 0 | |a LAPLACIANS |
| 690 | 1 | 0 | |a NON-CONFORMING FINITE ELEMENTS |
| 690 | 1 | 0 | |a NONCONFORMING FINITE ELEMENT |
| 690 | 1 | 0 | |a NUMBER OF DEGREES OF FREEDOM |
| 690 | 1 | 0 | |a NUMERICAL EXAMPLE |
| 690 | 1 | 0 | |a POSTERIORI ERROR ESTIMATOR |
| 690 | 1 | 0 | |a THREE DIMENSIONS |
| 690 | 1 | 0 | |a UPPER BOUND |
| 690 | 1 | 0 | |a ERROR ANALYSIS |
| 690 | 1 | 0 | |a SWITCHING SYSTEMS |
| 690 | 1 | 0 | |a EIGENVALUES AND EIGENFUNCTIONS |
| 700 | 1 | |a Durán, R.G. | |
| 700 | 1 | |a Padra, C. | |
| 773 | 0 | |d 2012 |g v. 62 |h pp. 580-591 |k n. 5 |p Appl Numer Math |x 01689274 |w (AR-BaUEN)CENRE-3774 |t Applied Numerical Mathematics | |
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| 856 | 4 | 0 | |u https://doi.org/10.1016/j.apnum.2012.01.005 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_01689274_v62_n5_p580_Dari |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01689274_v62_n5_p580_Dari |y Registro en la Biblioteca Digital |
| 961 | |a paper_01689274_v62_n5_p580_Dari |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 70609 | ||