孟兆良

个人信息Personal Information

副教授

硕士生导师

性别:男

毕业院校:大连理工大学

学位:博士

所在单位:数学科学学院

学科:计算数学

电子邮箱:mzhl@dlut.edu.cn

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A C-0-NONCONFORMING QUADRILATERAL FINITE ELEMENT FOR THE FOURTH-ORDER ELLIPTIC SINGULAR PERTURBATION PROBLEM

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论文类型:期刊论文

第一作者:Bao, Yuan

通讯作者:Meng, ZL (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.

合写作者:Meng, Zhaoliang,Luo, Zhongxuan

发表时间:2018-12-11

发表刊物:ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

收录刊物:SCIE

卷号:52

期号:5

页面范围:1981-2001

ISSN号:0764-583X

关键字:Singular perturbation problem; quadrilateral element; uniformly convergent

摘要:In this paper, a C-0 nonconforming quadrilateral element is proposed to solve the fourthorder elliptic singular perturbation problem. For each convex quadrilateral Q, the shape function space is the union of S-2(1) (Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.