A finite volume scheme preserving extremum principle for convection-diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection-diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second-order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell-centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second-order accuracy. Copyright (C) 2017 John Wiley & Sons, Ltd.