This paper is aimed at developing new shape functions adapted to the scalar wave equation with smooth (possibly vanishing) coefficients and investigates 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 main theoretical result states that any given order of approximation can be achieved by an appropriate choice of parameters for the design of the shape functions. The convergence is studied with respect to the size of the domain, which is referred to in the literature as $$h$$h-convergence.
|Original language||English (US)|
|Number of pages||29|
|State||Published - Dec 1 2015|
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics