中文摘要：

本文提出了求解二阶椭圆问题的一类广义有限元方法，分析了广义有限元方法的优越性，证明了二阶椭圆问题的广义有限元方法具有比标准的Galerkin有限元方法更高阶的收敛速度，根据插值算子的性质，进一步证明了有限元解的亏量迭代校正收敛到广义有限元解，并用数值例子说明广义有限元方法是有效的．

英文摘要：

In this paper we present a generalized finite element method for solving second order elliptic problems and analyze the superiority of this method. We prove that the generalized finite element method of the second order elliptic problems has higher convergence rate than the standard Galerkin finite element method. And based on the nature of the interpolation operator, we further prove that the defect iterative sequence of the finite element solution converge to the generalized finite element solution. Some numerical examples illustrate the generalized finite element method is effective.