## Eigenvalue and eigenfunction error estimates for finite element formulations of linear hydroelasticity

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## Abstract:

Convergence of an approximate method for determining vibrational eigenpairs of an elastic solid containing an incompressible fluid is examined. The field variables are solid displacement and fluid pressure. We show that in suitable Sobolev spaces a variational formulation exists whose solution eigenvalues and eigenfunctions are identified with those of a compact operator. A nonconforming finite element approximation of this variational problem is described and optimal a priori error estimates are obtained for both the eigenvalues and eigenfunctions.## References

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## Additional Information

**Pat Ryan**- Affiliation: Lockheed Martin Missiles and Space, Sunnyvale, California
- Email: pat.ryan@lmco.com
- Received by editor(s): February 2, 1999
- Published electronically: November 27, 2000
- Additional Notes: This research was sponsored in part by funding from the United States Air Force.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp.
**70**(2001), 471-487 - MSC (2000): Primary 65N30, 70J30; Secondary 65N25, 74F10
- DOI: https://doi.org/10.1090/S0025-5718-00-01259-X
- MathSciNet review: 1813139