Comparison of pressure and displacement formulations for finite elements in linear time-harmonic acoustics

In this article, we compare the finite element solution of the pressure and the displacement formulations for the acoustic problem in the frequency domain. The Helmholtz differential equation is solved for both, the spectral and the source problems, and each of these is formulated in terms of pressure and displacement. The pressure formulation allows to use standard Lagrangian elements whereas Raviart-Thomas elements are applied for the displacement formulation. Both formulations are tested in several examples. It is shown that Raviart-Thomas elements account for a reasonable alternative to Lagrangian elements in some cases.