Bounds for theN lowest eigenvalues of fourth-order boundary value problems |
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Authors: | C Wieners |
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Affiliation: | (1) ICA, Universitat Stuttgart, Pfaffenwaldring 27, D-70550 Stuttgart, Germany |
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Abstract: | We describe a method for the calculation of theN lowest eigenvalues of fourth-order problems inH
0
2
(Ω). In order to obtain small error bounds, we compute the defects inH
−2(Ω) and, to obtain a bound for the rest of the spectrum, we use a boundary homotopy method. As an example, we compute strict
error bounds (using interval arithmetic to control rounding errors) for the 100 lowest eigenvalues of the clamped plate problem
in the unit square. Applying symmetry properties, we prove the existence of double eigenvalues. |
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Keywords: | 65N25 |
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