An $hp$ Finite Element Method to Solve a Fluid-Solid Vibration Problem - Padra, Claudio; Rodríguez, Rodolfo; Scheble, Mario (SIAM journal on scientific computing, 2012)
This paper deals with a two-dimensional fluid-solid vibration problem arising from nuclear engineering: the vibration of elastically mounted tubes immersed in a cavity filled with fluid. A convenient variational formulation of this problem, valid for compressible and incompressible fluids, is introduced. An $hp$ finite element method is used for its discretization, which leads to a well posed matrix eigenvalue problem. Optimal order a priori error estimates are proved for eigenfunctions and eigenvalues. Then, local a posteriori error indicators are defined and its efficiency and reliability are studied. An adaptive scheme driven by these indicators is proposed and numerically tested. [PUBLICATION ABSTRACT]