非线性对流扩散方程沿特征线的多步有限体积元格式

A MULTISTEP FINITE VOLUME ELEMENT SCHEME ALONG CHARACTERISTICS FOR NONLINEAR CONVECTION DIFFUSION PROBLEMS

对于二维非线性对流扩散方程构造了沿特征线方向的多步有限体积元格式,关于空间采用二次有限体积元方法离散,关于时间采用多步法进行离散,获得了O(△t^2+h^2)形式的误差估计。本文最后给出的数值算例表明了方法的有效性。

A multistep finite volume element scheme along characteristics for two dimensional nonlinear convection diffusion equations is considered. The equations are discretized by quadratic finite volume element methods in space and by multistep methods in time. The error estimation which is O(△t^2+h^2) has been proved. A numerical example is given at the end to show the efficiency of the methods.