Eigenvalue and eigenfunction error estimates for finite element formulations of linear hydroelasticity
The author examines the convergence of an approximate method for determining vibrational eigenpairs of an elastic solid containing an incompressible fluid. (The field variables are solid displacement and fluid pressure.) He shows that in a suitable Sobolev space a variational formulation exists whose solution eigenvalues and eigenfunctions are identified with those of a compact operator, describes a nonconforming finite element approximation of this variational problem, and obtains optimal a priori error estimates for both the eigenvalues and eigenfunctions.
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