THE DEFECT ITERATION OF THE FINITE ELEMENT FOR ELLIPTIC BOUNDARY VALUE PROBLEMS AND PETROV-GALERKIN APPROXIMATION

查看全文 作　　者：Gao, JB;Yang, YD;Shih, TM 机构地区：[1]Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China;[2]Guizhou Normal Univ, Dept Math, Guiyang 550001, Peoples R China;[3]Hong Kong Polytech Univ, Dept Math Appl, Hong Kong, Peoples R China; 出　　处：《Journal of Computational Mathematics》索引1998年第16卷第2期,共13页 摘　　要：In this paper we introduce a Petrov-Galerkin approximation model to the solution of linear and semi-linear elliptic boundary value problems in which piecewise quadratic polynomial space and piecewise linear 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 attained in this Petrov-Galerkin model. Based on the so-called 'contractivity' of the interpolation operator, we further prove that the defect iterative sequence of the linear finite element solution converge to the proposed Petrov-Galerkin approximate sohution. 关 键 词：PETROV-GALERKIN APPROXIMATION DEFECT ITERATION correction INTERPOLATION OPERATOR