An operator splitting method for nonlinear convection-diffusion equations

被引:52
作者
Karlsen, KH [1 ]
Risebro, NH [1 ]
机构
[1] UNIV OSLO, DEPT MATH, N-0316 OSLO, NORWAY
关键词
SCALAR CONSERVATION-LAWS;
D O I
10.1007/s002110050291
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present a semi-discrete method for constructing approximate solutions to the initial value problem for the m-dimensional convection-diffusion equation u(t) + del.f(u) = epsilon Delta u. The method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation. In the case m > 1, dimensional splitting is used to reduce the m-dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence of approximate solutions which converges to the exact solution. Finally, a fully discrete method is analyzed, and demonstrated in the case of one and two space dimensions.
引用
收藏
页码:365 / 382
页数:18
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