Abstract
We propose a characteristic Galerkin scheme using B-spline basis functions for one-dimensional advection diffusion problems. One of significant features of the B-spline basis functions is that the B-spline basis functions of p degrees have at most C^p-1 continuous derivatives although classical finite elements based on Lagrange polynomials have only C^0 continuous derivatives. The feature works better for the characteristic Galerkin scheme. In order to confirm effectivity of the present scheme, we perform some numerical experiments and compare results of the present scheme with the SUPG scheme using the same basis functions.
