A two-grid scheme for characteristics finite-element solution of nonlinear convection-dominated diffusion equations was constructed. The L2 and H1 error estimates of the scheme were derived. A numerical example was also presented. The scheme involves solving one small, nonlinear problem on the coarse-grid system, one linear problem on the fine-grid system. The error estimates and the numerical example show that the new scheme is efficient to the nonlinear convection-dominated diffusion equations.

An information system is one of the very important mathematical models in the field of artificial intelligence. The notion of an information system homomorphism as a kind of tool to study the relation between two information systems was introduced in J.W. Grzymala-Busse (Algebraic properties of knowledge representation systems, in: Proceedings of the ACM SIGART International Symposium on Methodologies for Intelligent Systems, Knoxville, 1986, pp. 432

讨论了一类耗散发展方程时间离散化之后惯性流形的存在性。证明了如果时间步长充分小，且主算子A满足一个谱间隔条件，则所讨论的发展方程的一个简单差分格式存在一个惯性流形Mh．与Demengel F。的研究结果相比较，不仅简化了存在性证明，而且所建立的理论适用于更一般的非线性项。更进一步。在所建立的框架下，可以构造一个惯性流形序列（MhM），在某种意义下，当M-∞时MhM→Mh当h趋于零时Mh的收敛性以及理论应用将在第Ⅱ部分讨论。

研究热传导方程在一类非局部时间的边界条件下非线性热源的反演问题，文中应用Sobolev紧性方法证明了热源在Hōlder空间中的（关于时间的）局部存在性。

The two-grid finite element approximation to the stream function form of the stationary Navier-Stokes equations was analyzed. The algorithms involve solving one small, nonlinear coarse mesh system, one linear problem on the fine mesh system, and a linear correct problem on the coarse mesh. The algorithms with the correct problem and without the correct problem were discussed. The algorithms produce an approximate solution with the optimal, asymptotic accuracy for any fixed Reynolds number.