Quadrature-free characteristic methods for convection-diffusion problems

Galerkin-characteristics finite element method is a powerful numerical procedure for convection-diffusion problems even in the convection-dominated case. It is, however, reported that rough numerical integration for composite terms ruins the convergence property. In this paper we discuss two ways to avoid numerical quadrature referring to the recent results. One way is to use the lumping technique. A Galerkin-characteristics finite element scheme of lumped mass type is considered. The other way is to use a finite difference method derived from a Galerkin-characteristics finite element scheme. For these schemes the stability and convergence are discussed.