带有不连续系数的线性输运方程差分格式的收敛性

提出了一个基于三角形网格的显式差分格式逼近带有不连续系数的线性输运方程. 通过对数值解的有界性、TVD(total variation decreasing)和空间、时间方向的平移估计, 利用Kolmogorov紧性原理证明了数值解在L¹_loc模下收敛于初值问题的唯一弱解.从而得到了初值问题解的存在唯一性和关于初值的稳定性. 数值算例表明本文提出的格式计算方便而且比 Lax-Friedrichs格式更有效.  

CONVERGENCE OF DIFFERENCE SCHEME FOR LINEAR TRANSPORT EQUATION WITH DISCONTINUOUS COEFFICIENT

An explicit finite difference scheme for the linear transport equation is proposed. The scheme is built on triangular meshes. Based on the L^∞-bounds, TVD(total variation decreasing) and translation estimates of numerical solution, it is shown by means of Kolmogorov compactness method that the numerical solution converges to the weak solution of the initial value problem in the L¹_loc-norm. The theoretical results show that there exists a unique weak solution to the initial value problem which has the following properties: TVD, stable with respect to initial data. Several numerical experiments are presented to support our theoretical results. The numerical results also show that the method in this paper is convenient for computing and more effective than Lax-Friedrichs scheme.