Numerical Solution of Convection-Diffusion Equations Using a Nonlinear Method of Upwind Type

This paper is devoted to the numerical solution of convection-diffusion equations using the Mizukami-Hughes method which is a nonlinear method of upwind type using conforming piecewise linear triangular finite elements. We extend this method 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.