zbMATH — the first resource for mathematics

A remark on spurious eigenvalues in a square. (English) Zbl 0941.65109
Summary: We study the finite element approximation of the eigensolutions of a second-order problem in a square arising in fluid-structure interaction. We analyze the schemes described by H. C. Chen and R. L. Taylor [Int. J. Numer. Methods Eng. 29, No. 4, 683-698 (1990; Zbl 0724.73173)] and show that, when a uniform mesh is used, the first two methods produce spurious eigenmodes of different nature, while the third one provides eigensolutions converging to the continuous ones.
Reviewer: Reviewer (Berlin)

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs
Full Text: DOI
[1] Chen, H.; Taylor, R., Vibration analysis of fluid-solid systems using a finite element displacement formulation, Int. J. numer. methods eng., 29, 683-698, (1990) · Zbl 0724.73173
[2] D. Boffi, P. Fernandes, L. Gastaldi and I. Perugia, Computational models of electromagnetic resonators: Analysis of edge element approximation, SIAM Journal of Numer. An. (submitted).
[3] D. Boffi, F. Brezzi and L. Gastaldi, On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form, Math. Comp. (submitted). · Zbl 0938.65126
[4] Bermúdez, I.; Durán, R.; Muschietti, A.; Rodríguez, R.; Solomin, J., Finite element vibration analysis of fluid-solid systems without spurious modes, SIAM J. numer. anal., 32, 1280-1295, (1995) · Zbl 0833.73050
[5] Brezzi, F.; Fortin, M., Mixed and hybrid finite element methods, (1991), Springer-Verlag New York · Zbl 0788.73002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.