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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)

MSC:
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
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[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
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