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A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. (English) Zbl 0863.73055
Summary: 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 for the Helmholtz equation such that the pollution effect is minimal.
MSC:
74S05Finite element methods in solid mechanics
74J20Wave scattering (solid mechanics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)