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

Author: Pat Ryan
Journal: Math. Comp. 70 (2001), 471-487
MSC (2000): Primary 65N30, 70J30; Secondary 65N25, 74F10
Published electronically: November 27, 2000
MathSciNet review: 1813139
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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.

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Additional Information

Pat Ryan
Affiliation: Lockheed Martin Missiles and Space, Sunnyvale, California

Keywords: Hydroelasticity, finite element, eigenvalue, error estimates
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.
Article copyright: © Copyright 2000 American Mathematical Society