On the pollution effect in FE solutions of the 3D-Helmholtz equation Original Research Article

We study convergence of the FEM for a 3D-problem of rigid scattering. Using separation of variables, analytical results are presented for stability and error estimation for an h-version Galerkin FEM with mesh-refinement in radial direction. We prove an upper bound that contains a pollution term similar to previous results in 1D and 2D. This estimate is evaluated computationally using a 3D FEM-IEM (infinite elements) implementation. The tabulated and plotted errors show the theoretically predicted pollution effect in the FE-error.