有限元超收敛研究的新想法

A New Idea on Superconvergence Research in Finite Elements

简述了有限元超收敛研究的一种新想法 ,即在单元正交展开的余项中添加若干待定低次项 ,使此余项在一个单元上满足更多的正交性条件 ,并得到所需的超接近于有限元解uh的逼近函数uI .由此导出了一些新的超收敛结果 .

A new idea on superconvergence research in finite element methods is proposed. The idea is to add some lower degree terms in the remainder of orthogonal expansion in an element so that the remainder satisfies more orthogonality conditions in the element, and get a desired superclose funtionu I to finite element solution u h. Thus, several new superconvergence results are derived.