中文摘要：

对给定的具有光滑边界Γ的区域Ω ＊R^l（l=1,2,3）及时间区间（O,T],考虑如下的对流占优Sobolev方程：

英文摘要：

In this paper,an expanded characteristics-mixed finite element method is used to simulate Sobolev equations with convection term.The method is a combination of the characteristics line method and the expanded mixed finite element method.The scheme is stable since fluid is transported along the approximate characteristics on the discrete level.At the same time it expands the standard mixed finite element method in the sense that three variables：the scalar unknown, its gradient and its flux are explicitly treated.Moreover,theoretical analysis and numerical example show that the method is stable and its L^2-error estimate is optimal.