Three-dimensional dispersion analysis and stabilized finite element methods for acoustics

Galerkin/least-squares and Galerkin gradient/least-squares stand out among several approaches designed to improve the numerical solution accuracy and counteract the pollution effect by adding terms to the standard Galerkin formulation. These added terms are multiplied by a 'stability parameter', which must be properly defined. In this paper, an original three-dimensional dispersion analysis is performed for the Helmholtz equation, together with the determination of the three-dimensional stability parameters for structured and unstructured meshes. Numerical experiments show the relative efficiency of the proposed methods for solving acoustic problems arising from industry.