中文摘要：

这份报纸开发一个新方法在二和三种尺寸在矩形的格子上分析有限元素方法的重申的缺点修正计划的集中。主要想法是提出精力内部的产品和精力(半) 标准进矩阵形式。然后，包含的二关键不平等的二个常数是 min，二的最大特征值分别地联系概括特征值问题。这二个概括特征值问题的元素水平上的本地版本确切被解决突然地获得(更低) 这二个常数的上面的界限。这和为重申的答案的一些必要观察在减少的 2D 和单调建立集中在 3D 的性质。为二种尺寸，结果此处在文学改进那些；为三种尺寸，结果此处是新的。数字结果被介绍检验理论结果。[从作者抽象]

英文摘要：

This paper develops a new method to analyze convergence of the iterated defect correction scheme of finite element methods on rectangular grids in both two and three dimensions. The main idea is to formulate energy inner products and energy （semi）norms into matrix forms. Then, two constants of two key inequalities involved are min and max eigenvalues of two associated generalized eigenvalue problems, respectively. Local versions on the element level of these two generalized eigenvalue problems are exactly solved to obtain sharp （lower） upper bounds of these two constants. This and some essential observations for iterated solutions establish convergence in 2D and the monotone decreasing property in 3D. For two dimensions the results herein improve those in literature; for three dimensions the results herein are new. Numerical results are presented to examine theoretical results.