Characteristic Finite Element Method And Error Analysis For Nonlinear Convection Diffusion Equation

Convection diffusion equation is a kind of basic equation of motion, it can describe the quality,the heat transport problems,reaction-diffusion process and many other physical phenomena. Therefore, it is very meaningful both in theoretical and practical points to find a steady and rapid numerical method to solve these kind of equations.In this paper, an implicit characteristic finite element scheme is constructed to solve such nonlinear diffusion equation and the convergence of the scheme is studied. For nonlinear terms b=b(x,t,u,▽u), f= f(x,t,u,▽u), we get the L2(Ω) norm sub-optimal and the H1(Ω) norm optimal error estimates. And when b=b(x,t,u), f=f(x,t,u), the L2(Ω) norm and H1(Ω) norm optimal error estimates are obtained at the same time. The results show that it is very effective for using this method to solve nonlinear convection diffusion equation.