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A numerical study of a spectral problem in solid‐fluid type structures
Author(s) -
Conca Carlos,
Durán Mario
Publication year - 1995
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690110409
Subject(s) - mathematics , eigenvalues and eigenvectors , compressibility , quadratic equation , mathematical analysis , degree (music) , type (biology) , vibration , numerical analysis , geometry , physics , mechanics , ecology , quantum mechanics , biology , acoustics
This article presents a numerical study of a spectral problem that models the vibrations of a solid–fluid structure. It is a quadratic eigenvalue problem involving incompressible Stokes equations. In its numerical approximation we use Lagrange finite elements. To approximate the velocity, degree 2 polynomials on triangles are used, and for the pressure, degree 1 polynomials. The numerical results obtained confirm the theory, as they show in particular that the known theoretical bound for the maximum number of nonreal eigenvalues admitted by such a system is optimal. The results also take account of the dependence of vibration frequencies with respect to determined physical parameters, which have a bearing on the model. © 1995 John Wiley & Sons, Inc.