Asymptotic lower bounds for eigenvalues by nonconforming finite element methods

Electronic Transactions on Numerical Analysis

Volumn 17, Issue , 2004, Pages 93-101

  Armentano, María G ^a   Durán, Ricardo G ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

Eigenvalue problems; Finite elements; Nonconforming methods

Indexed keywords

EID: 3042677699     PISSN: 10689613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. G. ACOSTA, R. G. DUŔAN, The maximum angle condition for mixed and non conforming elements: Application to the Stokes equations, SIAM J. Numer. Anal., 37 (2000), pp. 18-36.
2. M. G. ARMENTANO AND R. G. DUŔAN, Mass-Lumping or not Mass-Lumping for eigenvalue problems, Numer. Methods Partial Differential Equations, 19 (2003), pp. 653-664.
3. I. BABUSKA, R. B. KELLOG, J. PITKARANTA, Direct and Inverse Error Estimates for Finite Elements with Mesh Refinement, Numer. Math., 33 (1979), pp. 447-471.
4. I. BABUSKA AND J. OSBORN, Eigenvalue Problems, Handbook of Numerical Analysis, vol. II, Finite Element Methods (Part 1), 1991.
5. S. C. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, Springer-Verlag, New York, 1994.
6. R. G. DUŔAN, L. GASTALDI AND C. PADRA, A posteriori error estimators for mixed approximations of eigenvalue problems, Math. Models Methods Appl. Sci., 9 (1999), pp. 1165-1178.
7. G. E. FORSYTHE, Asymptotic lower bounds for the frequencies of certain polygonal membranes, Pacific J. Math., 4 (1954), pp. 467-480.
8. G. E. FORSYTHE, Asymptotic lower bounds for the fundamental frequency of convex membranes, Pacific J. Math., 5 (1955), pp. 691-702.
9. C. A. GRIFFITH AND M. L. LAPIDUS, Computer graphics and the eigenfunctions for the Koch snowflake drum. Andersson, S. I. et al., eds., Progress in inverse spectral geometry, Birkhuser, Trends in Mathematics, 1997, pp. 95-113.
10. P. GRISVARD, Elliptic Problems in Nonsmooth Domain, Pitman, Boston, 1985.
11. M. L. LAPIDUS, J. W. NEUBERGER, R. J. RENKA AND C. A. GRIFFITH, Snowflake harmonics and computer graphics: Numerical computation of spectra on fractal drums, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 6 (1996), pp. 1185-1210.
12. H. F. WEINBERGER, Upper and lower bounds for eigenvalues by finite difference methods, Comm. Pure Appl. Math., 9 (1956), pp. 613-623.
13. H. F. WEINBERGER, Lower bounds for heigher eigenvalues by finite difference methods, Pacific J. Math., 8 (1958), pp. 339-368.
14. O. WIDLUND, On best error bounds for approximation by piecewise polynomial functions, Numer. Math., 27 (1977), pp. 327-338.