A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution

When using the Galerkin FEM for solving the Helmholtz equation in two dimensions, the error of the corresponding solution differs substantially from the error of the best approximation, and this effect increases with higher wave number k. In this paper we will design a Generalized Finite Element Method (GFEM) for the Helmholtz equation such that the pollution effect is minimal