中文摘要：

这份报纸是在各向异性的网孔下面学习矩形的有限元素的集中和 superconvergence。由直角的扩大方法使用，各向异性的 Lagrange 插值被介绍。有所有可能的形状功能空格的 Lagrange 矩形的元素的家庭被认为家庭，它盖住中间的家庭，张肌产品家庭和易遇奇缘的运气。各向异性的插值错误估计为任何顺序 Sobolev 标准成立，这被显示出。我们以一个统一方法扩大集中和矩形的有限元素的 superconvergence 结果到任意的矩形的网孔。[从作者抽象]

英文摘要：

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.