  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.
