A high-order upwind method for the convection-diffusion problem

✍ Scribed by Dong Liang; Weidong Zhao

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 643 KB
• Volume: 147
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(97)00004-2

✦ Synopsis

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 estimates O(h'~~c'"'~~,,) in d' lscrete L', H1 and L' norms, in which the constants in O(h'ljc'4'11,,) do not depend on the diffusion coefficient a, the velocity b, the solution c 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.