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论文类型：期刊论文

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.