一类广义插值函数与广义有限元方法的后验估计  

A GENERALIZED INTERPOLATION AND ITS APPLICATION TO A GENERALIZED FINITE ELEMENT METHOD

作　　者：舒适[1] 黄云清[1] 喻海元[1] 

机构地区：[1]湘潭大学数学系,计算与应用数学研究所,湘潭411105

出　　处：《计算数学》2000年第1期113-120,共8页Mathematica Numerica Sinica

基　　金：国家973"大规模科学计算研究"基金

摘　　要：In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.In this paper, we discuss a generalized finite element interpolation problem and obtain the asymptotic expansion of the interpolation function. Based on these results, the error asymptotic expansion and superconvergence result of the generalized finite element approximation are derived. Finallym using the Superconvergent Patch Recovery Technique (SPR) proposed by Zienkiewicz & Zhu, we get the superconvergent recovery approximation and the posteriori error estimates to the flux. The numerical test convinced our analysis.

关 键 词：广义有限元 后验估计 渐近展开式 广义插值函数 

分 类 号：O241[理学—计算数学]