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- W2096390973 abstract "This paper is the second part of a two-part paper treating a non-self-adjointquadratic eigenvalue problem for the linear stability ofsolutions to the Taylor-Couette problem for flow of a viscous liquid in a deformablecylinder, with the cylinder modelled as a membrane. The first part formulated the problem, analyzed it,and presented computations. In this second part,we first give a weak formulation of the problem, carefully contrived so thatthe pressure boundary terms are eliminated fromthe equations. We prove that the bilinear formsappearing in the weak formulation satisfy continuous inf-supconditions. We combine a Fourier expansion with the finite element methodto produce a discrete problem satisfying discrete inf-supconditions. Finally, the Galerkin approximationtheory for polynomial eigenvalue problems is applied to prove convergence of the spectrum." @default.
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- W2096390973 date "2009-01-01" @default.
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- W2096390973 title "A Non-Self-Adjoint Quadratic Eigenvalue Problem Describing a Fluid-Solid Interaction Part II: Analysis of Convergence" @default.
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- W2096390973 doi "https://doi.org/10.3934/cpaa.2009.8.143" @default.
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