 
Summary: An hp finite element adaptive method to compute the vibration
modes of a fluidsolid coupled system
M. G. Armentano 1, C. Padra 2, R. Rodr´iguez 3 and M. Scheble 2,
1 Departamento de Matem´atica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires,
1428, Buenos Aires, Argentina
2 Centro At´omico Bariloche, 4800, Bariloche, Argentina
3 CI2MA, Departamento de Ingenier´ia Matem´atica, Universidad de Concepci´on, Casilla 160C, Concepci´on,
Chile
SUMMARY
In this paper we propose an hp finite element method to solve a twodimensional fluidstructure
vibration problem. This problem arises from the computation of the vibration modes of a bundle of
parallel tubes immersed in an incompressible fluid. We use a residualtype a posteriori error indicator
to guide an hp adaptive algorithm. Since the tubes are allowed to be different, the weak formulation
is a nonstandard generalized eigenvalue problem. This feature is inherited by the algebraic system
obtained by the discretization process. We introduce an algebraic technique to solve this particular
spectral problem. We report several numerical tests which allow us to assess the performance of the
scheme. Copyright c 2000 John Wiley & Sons, Ltd.
key words: fluid structure interaction, vibration problem, hp finite element adaptive method
1. INTRODUCTION
In this work we consider an hp finite element adaptive scheme for solving a fluidstructure
