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Lower bounds for eigenvalues by nonconforming FEM on convex domain. (English) Zbl 1232.35105

Todorov, Michail D. (ed.) et al., Application of mathematics in technical and natural sciences. Proceedings of the 2nd international conference (AMiTaNS’10), Sozopol, Bulgaria, June 21–26, 2010. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0856-2/pbk). AIP Conference Proceedings 1301, 361-369 (2010).
Summary: We analyze the approximations of second order eigenvalue problems (EVPs). The nonconforming piecewise linear finite element with integral degrees of freedom is used. We prove that the eigenvalues computed by means of this element on convex domain are smaller than the exact ones if the mesh size is small enough. Some numerical results are also given.
For the entire collection see [Zbl 1228.00019].

MSC:

35P15 Estimates of eigenvalues in context of PDEs
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
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