半线性椭圆问题Petrov-Galerkin逼近及亏量迭代  

PETROV-GALERKIN APPROXIMATION OF THE SEMI-LINEAR ELLIPTIC AND THE DEFECT ITERATION

作　　者：司红颖[1] 陈绍春[2] 

机构地区：[1]商丘师范学院数学系,河南商丘476000 [2]郑州大学数学系,郑州450052

出　　处：《计算数学》2014年第3期316-324,共9页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.11071226);河南省自然科学基金(No.132300410272)

摘　　要：本文考虑了二阶半线性椭圆问题的Petrov-Galerkin逼近格式,用双二次多项式空间作为形函数空间,用双线性多项式空间作为试探函数空间,证明了此逼近格式与标准的二次有限元逼近格式有同样的收敛阶.并且根据插值算子的逼近性质,进一步证明了半线性有限元解的亏量迭代序列收敛到Petrov-Galerkin解.In this paper we introduce a Petrov-Galerkin boundary value problems in which biquadratic approximation model to semi-linear elliptic polynomial space and bilinear polynomial space are used as the shape function space and the test function space, respectively. We prove that the approximation order of the standard quadratic finite element can be abtained by this Petrov-Calerkin model. Based on the socalled “contractivity” of the interpolation operator, we further prove that the defect iterative sequence of the semilinear finite element solution converse to the proposed Petrov-Galerkin approximate solution.

关 键 词：Petrov-Galerkin逼近 亏量迭代 插值算子 

分 类 号：O175.25[理学—数学]