Characteristic Galerkin scheme using B-spline basis functions for advection diffusion problems

Abstract

We propose a characteristic Galerkin scheme using B-spline basis functions for 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 C⁰ 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.