非协调区域分解Lagrange乘子法的超收敛

本文讨论分析非协调区域分解Ｌａｇｒａｎｇｅ乘子法对二阶椭圆型方程Ｄｉｒｉｃｈｌｅｔ问题的有限元超收敛现象。文中通过利用积分恒等式，适宜地引进Ｌ２投影过渡以及高次插值后处理等技巧，经过一系列误差分析及估计，得到了高出半阶的超收敛结果，实现了非协调区域分解法与高精度算法的结合。

SUPERCONVERGENCE OF THE NONCONFORMINGDOMAIN DECOMPOSED FINITE ELEMENTMETHOD WITH LAGRANGE MULTIPLIERS

In this paper, we study the superconvergence phenomena of the non-conforming domain de-omposed finite element method with Lagrange multipliers to a 2-order elliptic problem. The main ideaof this chapter is to achieve the combination of parallel computational method with the higher accuracytechnique by interpolation finite element postprocessing which is implemented only by using a simple andonvenient algorithm. The higher accuracy of one and half an order have been obtained by using integralidentity, introducing L2 projection, postprocessing of interpolation finite element and so on.