Abstract
The paper deals with nonconforming finite element methods for approximating fourth order eigenvalue problems of typeΔ 2 w=λΔw. The methods are handled within an abstract Hilbert space framework which is a special case of the discrete approximation schemes introduced by Stummel and Grigorieff. This leads to qualitative spectral convergence under rather weak conditions guaranteeing the basic properties of consistency and discrete compactness for the nonconforming methods. Further asymptotic error estimates for eigenvalues and eigenfunctions are derived in terms of the given orders of approximability and nonconformity. These results can be applied to various nonconforming finite elements used by Adini, Morley, Zienkiewicz, de Veubeke e.a. This is carried out for the simple elements of Adini and Morley and is illustrated by some numerical results at the end.
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Rannacher, R. Nonconforming finite element methods for eigenvalue problems in linear plate theory. Numer. Math. 33, 23–42 (1979). https://doi.org/10.1007/BF01396493
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DOI: https://doi.org/10.1007/BF01396493