Numerical solution of convection-diffusion equations using a nonlinear method of upwind type

• ID: 2560, RIV: 10051724
• ISSN: 0885-7474, ISBN: not specified
• source: Journal of Scientific Computing
• keywords: finite element method; convection-diffusion equation; Mizukami-Hughes method; upwind; maximum principle
• authors: Petr Knobloch
• authors from KNM: Knobloch Petr

Abstract

This paper is devoted to the numerical solution of convection-diffusion equations using the Mizukami-Hughes method. The method is extended to the whole range of the diffusion parameter whereas the original method was introduced for the convection-dominated regime only. We prove that the extended method satisfies the discrete maximum principle and illustrate its properties by means of numerical results.