中文摘要：

1 引言 求解偏微分方程的混合元方法在实际问题（如油藏和地下水的数值模拟）中有广泛的应用．与标准的有限元相比，混合元方法可以同时求解两个变量即压力和流速的近似，而且能保持问题的局部守恒性，从而得到了更好的结果（如Arnold）．现已有许多文献使用混合元法求解线性的（如[2]），拟线性的（如Milner）和非线性的（如Park）二阶椭圆问题．

英文摘要：

A two-grid algorithm for solving mixed finite element approximation of two-dimensional semilinear elliptic equations is presented. This method involves the solution of a nonlinear system on coarse grid of size H and two linear corrections on the fine grid of size h. Existence and uniqueness of the approximation are proved and error estimates in L^2 are demonstrated for both the scalar and vector functions approximated by the algorithm. Error estimate for the scalar function is also derived in L^θ（2 ≤ θ 〈∞）. The above estimates are useful for determining an appropriate H for the coarse grid problem.