具有积分型边界条件的抛物方程一个新混合元方法的超收敛分析

摘要

The main aim of this paper is to propose a new mixed finite element method based on the bilinear element and the lowest order Nédélec′s element ( )Q11/Q01 × Q10 for a class of parabolic problems with integral boundary condition. This method has the advantages of small total degrees of freedom and satisfies the BB condition. At the same time,for semi-discrete scheme,by use of the special high accuracy analysis of these two elements,and derivative transfer technique,the original variable u in H1-norm and flux p=∇u in L2-norm are derived with element interpolations instead of the Ritz projections which are indispensable in the conventional finite element analysis. Furthermore,the corresponding global super-convergence results are obtained through interpolated post processing approach. The results presented herein have never been seen in the previous literature.%主要目的是对一类具有积分型边界条件的抛物方程，基于双线性元及最低阶Nédélec′s元()Q11/Q01× Q10提出了一个新的混合有限元方法，它具有总体自由度小且满足BB条件等优势。同时借助于这两个单元的特殊高精度分析及导数转移技巧，在抛弃传统的有限元分析中必不可少的Ritz投影的前提下，直接利用单元插值导出了在半离散格式下原始变量u在H1-模及流量 p=∇u在L2-模意义下的超逼近性质。进一步地，通过插值后处理技术，得到了相应的整体超收敛结果。这里所得的结果是以往文献尚未涉及的。