Nonlinear diffusion and discrete maximum principle for stabilized Galerkin approximations of the convection-diffusion-reaction equation

摘要

We investigate stabilized Galerkin approximations of linear and nonlinear convection-diffusion-reaction equations. We derive nonlinear streamline and cross-wind diffusion methods that guarantee a discrete maximum principle for Strictly acute meshes and first order polynomial interpolation. For pure convection-diffusion problems, the discrete Maximum principle is achieved using a nonlinear cross-wind diffusion factor that depends on the angle between the Discrete solution and the flow velocity.