中文摘要：

针对一类非线性抛物方程的混合元形式，本文提出了二重网格算法．该算法是在网格大小为H的粗网格上求解一个非线性系统，再在网格大小为h的细网格上进行两次线性计算．算法第二步和第三步的误差分别为O（△t^2＋h^（k＋1）＋H^（2k＋1），O（△t^2＋h^（k＋1）＋h^（-d/2）H^（4k＋4），其中k为逼近空间的多项式的次数，d为空间维数．该估计对H的选取起了很大的作用．对于粗网格上的非线性计算，本文给出了L^p（2≤p〈∞）模误差估计．

英文摘要：

A two-grid algorithm for mixed finite element solution of nonlinear parabolic equations is presented in this paper. The algorithm involves solving one small nonlinear problem on the coarse grid of size H and two linear problems on the fine grid of size h. Error estimates are derived which demonstrate that the error is O（△t^2＋h^（k＋1）＋H^（2k＋1）,O（△t^2＋h^（k＋1）＋h^（-d/2）H^（4k＋4）, where k is the degree of the approximating space for the primary variable and d is spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problem. The error estimate in L^p for the nonlinear solution of the coarse grid is also presented.