A numerical comparison of finite element methods for the Helmholtz equation

Three finite element formulations for the solution of the Helmholtz equatio n are considered. The performance of these methods is compared by performin g a discrete dispersion analysis and by serving two canonical problems on n onuniform meshes. It is found that: (1) The scaled L-2 error for the Galerk in method, using linear interpolation functions, grows as k(kh)(2), indicat ing the pollution inherent in this method; (2) The Galerkin least squares m ethod is more accurate, but does display significant pollution error; (3) T he residual-based method of Oberai & Pinsky,(8) which was designed to be al most pollution-free for uniform meshes retains its accuracy on nonuniform m eshes; (4) The computational cost of implementing all these formulations is approximately the same.