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

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.

Keywords

• finite element method
• convection-diffusion equation
• Mizukami-Hughes method
• upwind
• maximum principle