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Eigenvalue and eigenfunction error estimates for finite element formulations of linear hydroelasticity
Author(s):
Pat
Ryan.
Journal:
Math. Comp.
70
(2001),
471-487.
MSC (2000):
Primary 65N30, 70J30;
Secondary 65N25, 74F10
Posted:
November 27, 2000
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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
Email:
pat.ryan@lmco.com
DOI:
10.1090/S0025-5718-00-01259-X
PII:
S 0025-5718(00)01259-X
Keywords:
Hydroelasticity,
finite element,
eigenvalue,
error estimates
Received by editor(s):
February 2, 1999
Posted:
November 27, 2000
Additional Notes:
This research was sponsored in part by funding from the United States Air Force.
Copyright of article:
Copyright
2000,
American Mathematical Society
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