• 论文 •

### 半线性椭圆问题Petrov-Galerkin逼近及亏量迭代

1. 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
• 收稿日期:2013-11-15 出版日期:2014-08-15 发布日期:2014-09-28
• 基金资助:

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

Si Hongying, Chen Shaochun. PETROV-GALERKIN APPROXIMATION OF THE SEMI-LINEAR ELLIPTIC AND THE DEFECT ITERATION[J]. Mathematica Numerica Sinica, 2014, 36(3): 316-324.

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

Si Hongying1, Chen Shaochun2

1. 1. Department of Mathematics, Shangqiu Normal University, Shangqiu 476000, Henan, China;
2. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
• Received:2013-11-15 Online:2014-08-15 Published:2014-09-28

In this paper we introduce a Petrov-Galerkin approximation model to semi-linear elliptic boundary value problems in which biquadratic 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-Galerkin model. Based on the so-called "contractivity" of the interpolation operator, we further prove that the defect iterative sequence of the semi-linear finite element solution converge to the proposed Petrov-Galerkin approximate solution.

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