Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-diffusion problems. The scheme i s unconditionally stable, independent of the diffusion coefficient, even in the case when numerical quadrature is used. The theoretical predictions ar e illustrated by a series of numerical experiments. For the periodic case, our results present a significant improvement on those given by Suli & Ware .