有限元反估计中常数C的上界

The upperbound of constant C in the inverse inequalities

反估计不等式在有限元分析中颇为重要 ,许多算法的收敛性结果的证明都要用到此类不等式 ,它涉及函数不同模之间的相互关系。此类结果曾被多次证明 ,但在已有的反估计不等式中 ,其估计式中皆含有一个未知的常数 C。文章用一种新方法证明反估计不等式 ,从而得到相应常数

The inverse inequalities,which deals with the relationship between the different moduli, are important in the finite element analysis, and they are used to prove the convergence results of some algorithms. Such inequalities had been proved more than one time. But in the known inverse inequalities there was an unknown constant C. In this paper, a new proof of the inverse inequalities is made, therefore the estimations of upperbounds of the constants are obtained.