A Posteriori Error Estimates and a Local Refinement Strategy for a Finite Element Method to Solve Structural-Acoustic Vibration Problems

This paper deals with an adaptive technique to compute structural-acoustic vibration modes. It is based on an a posteriori error estimator for a finite element method free of spurious or circulation nonzero-frequency modes. The estimator is shown to be equivalent, up to higher order terms, to the approximate eigenfunction error, measured in a useful norm; moreover, the equivalence constants are independent of the corresponding eigenvalue, the physical parameters, and the mesh size. This a posteriori error estimator yields global upper and local lower bounds for the error and, thus, it may be used to design adaptive algorithms. We propose a local refinement strategy based on this estimator and present a numerical test to assess the efficiency of this technique.