Abstract
Three finite element formulations for the solution of the Helmholtz equation are considered. The performance of these methods is compared by performing a discrete dispersion analysis and by solving two canonical problems on nonuniform meshes. It is found that: (1) The scaled L2 error for the Galerkin method, using linear interpolation functions, grows as k(kh)2, indicating the pollution inherent in this method; (2) The Galerkin least squares method is more accurate, but does display significant pollution error; (3) The residual-based method of Oberai & Pinsky,8 which was designed to be almost pollution-free for uniform meshes retains its accuracy on nonuniform meshes; (4) The computational cost of implementing all these formulations is approximately the same.
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