Dispersion analysis in scalar generalized finite element method

A semi-analytic technique for the dispersion analysis of scalar generalized finite element method (GFEM) that can be easily applied to higher dimensions and vector GFEM has been developed. The phase error simulation results validate the O([h/lambda]^2p) convergence rate of the Legendre polynomials. GFEM compared to FEM significantly suppresses the error for the higher orders. The phase error depends on the incident angle and it shows different behavior for each order. The error in discrete representation of the differential equation is shown to be related to the error in function representation. Results using different local approximation functions as well as generalization of the methodology to vector basis functions are presented.