中文摘要：

在这个工作，为非线性的寓言的问题的二格子的典型有限体积计划被考虑。在我们的算法，散开术语是由有限体积方法的 discretized，当时间的区别和移流术语被典型计划对待时。在关于系数和准确答案的一些条件下面，为数字答案的最佳的错误估计被获得。而且，有限体积方法包含与网孔尺寸 H 在粗糙的网孔上解决一个非线性的方程的 twogrid 特征，为有网孔尺寸 h = O ( H2 )的一个好网孔上的 Oseen 二格子的典型的有限的卷方法的一个大线性问题或为有网孔尺寸 h = O (鈭?日志 h 鈭? H3 )的一个好网孔上的牛顿二格子的典型的有限的卷方法的一个大线性问题。我们学习了的这些方法作为典型有限体积方法的提供一样的集中率，它涉及与网孔尺寸 h 在一个好网孔上解决一个大非线性的问题。一些数字结果被介绍表明建议方法的效率。[从作者抽象]

英文摘要：

In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.