Accurate pressure post-process of a finite element method for elastoacoustics

This paper deals with a post-process to obtain a more accurate approximation of the fluid pressure from a finite element computation of the vibration modes of a fluid-structure coupled system. The underlying finite element method, based on a displacement formulation for both media, consists of using Raviart-Thomas elements for the fluid combined with standard continuous elements for the solid. An easy to compute post-process of the pressure is derived. The relation between this post-process and an alternative finite element approximation of the problem based on discretizing the fluid pressure by enriched Crouzeix-Raviart elements is studied. Higher order estimates for the L(2) norm of the post-processed pressure are proved by exploiting this relation. As a by-product, higher order L(2) estimates for the solid displacements obtained with the original method are also proved.