NUMERICAL APPROXIMATION OF THE DISPLACEMENT FORMULATION OF THE AXISYMMETRIC ACOUSTIC VIBRATION PROBLEM

The aim of this paper is to study the numerical approximation of the displacement formulation of the acoustic eigenvalue problem in the axisymmetric case. We show that spurious eigenvalues appear when lowest order triangular Raviart-Thomas elements are used to discretize the problem. We propose an alternative weak formulation of the spectral problem which allows us to avoid this drawback. A finite element discretization based on the same finite elements is proposed and analyzed. Quasi-optimal order spectral convergence is proved, as well as absence of spurious modes. Numerical experiments are reported which agree with the theoretical results.