Characteristic Volume Method For One Kind Of Advection-Diffusion Equations

In this paper, the following halflinear advection-diffusion equations is simulated by two new methods called characteristic finite volume method and characteristic discontinuous finite volume method, which are combination of char-acteristic method and finite volume method. Our analysis shows that the latter method not only possess the advantages of discontinuous finite volume method, for example, high order accuracy, parallelizability and simplicity of space construction, it also inherits some features of characteristic method:it is stable and can smear sharp front of the solution. So it's a new and effective method for advection-diffusion equation. In the second chapter, by making the numerical analysis, we obtain the optimal error estimates of L2-norm and H1-norm about the unknow function. In the third chapter, by making the numerical analysis, we obtain the optimal error estimates of L2-norm and (?)·(?)1,h-norm about the unknow function. Then we simulate the following nonlinear advection-diffusion equation by discontinuous finite volume method based on the third chapter about halflinear advection-diffusion equations.The characteristic discontinuous finite volume proce-dures for this problem are proposed. And we propose the auxiliary formulation and give the error analysis. Numerical analysis shows that we can obtain the optimal error estimates of L2-norm and (?)·(?)1.h-norm about the unknown function by this method.