Interpolation properties of generalized plane waves

Abstract: This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence is shown with respect to the size of the domain considered. The new basis functions are then implemented in a numerical method to solve a scalar wave equation problem with a mixed boundary condition. The order of convergence of the method varies linearly with the one of the interpolation.