CONVERGENCE OF DIFFERENCE SCHEME FOR LINEAR TRANSPORT EQUATION WITH DISCONTINUOUS COEFFICIENT
带有不连续系数的线性输运方程差分格式的收敛性

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 L1loc-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.