A high-order upwind method for the convection-diffusion problem Original Research Article

In this paper, a high-order upwind method for the convection-diffusion problems is proposed. The scheme satisfies the maximum principle, overcomes numerical oscillation, and has astonishingly high-order computing accuracy. At the same time, the error estimatesO(h3‘c(4)‘0) in discreteL2,H1 andLx norms, in which the constants inO(h3‘c(4)‘0) do not depend on the diffusion coefficienta, the velocity b, the solutionc and the domain partition, are obtained by using a new analytic technique. Several numerical examples are given in order to demonstrate the efficiency of the method.