Two-grid Method for Characteristics Finite Volume Element of Nonlinear Convection-dominated Diffusion Equations

摘要

A characteristics finite volume element discretization technique based on two subspaces is presented for anonlinear convection-dominated diffusion equations. The solution of a nonlinear system on the fine space is composed ofsolving one small (nonlinear) system on the coarse space and alinear system on the fine space. Error estimates are derivedand numerical experiments are performed to validate theaccuracy and efficiency of our present scheme. It is shown boththeoretically and numerically, that the new scheme is efficientto the nonlinear convection-dominated diffusion equations.