Artículo
Armentano, M.G.; Durán, R.G. "Asymptotic lower bounds for eigenvalues by nonconforming finite element methods" (2004) Electronic Transactions on Numerical Analysis. 17:93-101
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Abstract:
We analyze the approximation obtained for the eigenvalues of the Laplace operator by the nonconforming piecewise linear finite element of Crouzeix-Raviart. For singular eigenfunctions, as those arising in nonconvex polygons, we prove that the eigenvalues obtained with this method give lower bounds of the exact eigenvalues when the mesh size is small enough.
Registro:
| Documento: | Artículo |
| Título: | Asymptotic lower bounds for eigenvalues by nonconforming finite element methods |
| Autor: | Armentano, M.G.; Durán, R.G. |
| Filiación: | Departamento de Matemática, Fac. de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina |
| Palabras clave: | Eigenvalue problems; Finite elements; Nonconforming methods |
| Año: | 2004 |
| Volumen: | 17 |
| Página de inicio: | 93 |
| Página de fin: | 101 |
| Título revista: | Electronic Transactions on Numerical Analysis |
| Título revista abreviado: | Electron. Trans. Numer. Anal. |
| ISSN: | 10689613 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano |
Referencias:
- Acosta, G., Duŕan, R.G., The maximum angle condition for mixed and non conforming elements: Application to the Stokes equations (2000) SIAM J. Numer. Anal., 37, pp. 18-36
- Armentano, M.G., Duŕan, R.G., Mass-Lumping or not Mass-Lumping for eigenvalue problems (2003) Numer. Methods Partial Differential Equations, 19, pp. 653-664
- Babuska, I., Kellog, R.B., Pitkaranta, J., Direct and Inverse Error Estimates for Finite Elements with Mesh Refinement (1979) Numer. Math., 33, pp. 447-471
- Babuska, I., Osborn, J., Eigenvalue Problems (1991) Handbook of Numerical Analysis, Vol. II, Finite Element Methods, 2 (1 PART)
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- Duŕan, R.G., Gastaldi, L., Padra, C., A posteriori error estimators for mixed approximations of eigenvalue problems (1999) Math. Models Methods Appl. Sci., 9, pp. 1165-1178
- Forsythe, G.E., Asymptotic lower bounds for the frequencies of certain polygonal membranes (1954) Pacific J. Math., 4, pp. 467-480
- Forsythe, G.E., Asymptotic lower bounds for the fundamental frequency of convex membranes (1955) Pacific J. Math., 5, pp. 691-702
- Griffith, C.A., Lapidus, M.L., Computer graphics and the eigenfunctions for the Koch snowflake drum (1997) Trends in Mathematics, pp. 95-113. , Andersson, S. I. et al., eds., Progress in inverse spectral geometry, Birkhuser
- Grisvard, P., (1985) Elliptic Problems in Nonsmooth Domain, , Pitman, Boston
- Lapidus, M.L., Neuberger, J.W., Renka, R.J., Griffith, C.A., Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums (1996) Internat. J. Bifur. Chaos Appl. Sci. Engrg., 6, pp. 1185-1210
- Weinberger, H.F., Upper and lower bounds for eigenvalues by finite difference methods (1956) Comm. Pure Appl. Math., 9, pp. 613-623
- Weinberger, H.F., Lower bounds for heigher eigenvalues by finite difference methods (1958) Pacific J. Math., 8, pp. 339-368
- Widlund, O., On best error bounds for approximation by piecewise polynomial functions (1977) Numer. Math., 27, pp. 327-338
Citas:
---------- APA ----------
Armentano, M.G. & Durán, R.G. (2004) . Asymptotic lower bounds for eigenvalues by nonconforming finite element methods. Electronic Transactions on Numerical Analysis, 17, 93-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano [ ]
---------- CHICAGO ----------
Armentano, M.G., Durán, R.G. "Asymptotic lower bounds for eigenvalues by nonconforming finite element methods" . Electronic Transactions on Numerical Analysis 17 (2004) : 93-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano [ ]
---------- MLA ----------
Armentano, M.G., Durán, R.G. "Asymptotic lower bounds for eigenvalues by nonconforming finite element methods" . Electronic Transactions on Numerical Analysis, vol. 17, 2004, pp. 93-101.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano [ ]
---------- VANCOUVER ----------
Armentano, M.G., Durán, R.G. Asymptotic lower bounds for eigenvalues by nonconforming finite element methods. Electron. Trans. Numer. Anal. 2004;17:93-101.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10689613_v17_n_p93_Armentano [ ]
