Element-Free Galerkin solutions for Helmholtz problems: fomulation and numerical assessment of the pollution effect

Abstract The Element-Free Galerkin Method (EFGM), a particular case of the meshless methods, is examined in its application to acoustic wave propagation addressed by the Helmholtz equation. Dispersion and pollution effects, two problems encountered by the classical numerical methods, are reviewed. Numerical tests on two-dimensional problems focus on the parameters governing the formulation of the EFGM. They also demonstrate that the EFGM is affected by dispersion and pollution effects as well as FEM, but these effects are rather low, showing that the EFGM is a promising method.

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