非稳态对流占优的对流-扩散问题的数值分析

由于边界层的存在，为数值求解非稳态对流占优的对流－扩散问题带来了困难，当用中心差分或标准有限元方法求解这类问题时，除非剖分足够细，否则就会出现非物理的震荡，使得数值解失真，而在高维问题时，常使得工作量大得不可接受，故使用ｐ－ｖｅｒｓｉｏｎ（多项式空间）加一指数函数的方法来求解非稳态对流占优的对流－扩散问题，除了理论分析外，并作了数值试验，得到了较满意的结果。

Numerical Analysis of Nonstationary Convection-Dominated Convection-Diffusion Problems

It is known that it is difficult to solve the nonstationary convection dominated convection diffusion problems numerically because of occurrence of the boundary or interior layers. The finite central difference method and standard finite element method fail to solve them, unless the discretization is fine enough to resolve the layers, and which usually make the discretization unacceptable. Here p version with a exponential function method is used to solve convection dominated convection diffusion problems. Some numerical tests are performed besides theoretical analysis and have satisfying results.