Two-grid method for characteristics finite volume element of nonlinear convection-dominated diffusion equations

A characteristics finite volume element discretization technique based on two subspaces is presented for a nonlinear convection-dominated diffusion equations. The solution of a nonlinear system on the fine space is composed of solving one small (nonlinear) system on the coarse space and a linear system on the fine space. Error estimates are derived and numerical experiments are performed to validate the accuracy and efficiency of our present scheme. It is shown both theoretically and numerically, that the new scheme is efficient to the nonlinear convection-dominated diffusion equations. © 2016, International Association of Engineers. All rights reserved.