Superconvergence of immersed finite element methods for interface problems

被引:0
作者
Waixiang Cao
Xu Zhang
Zhimin Zhang
机构
[1] Beijing Computational Science Research Center,Department of Mathematics and Statistics
[2] Mississippi State University,Department of Mathematics
[3] Wayne State University,undefined
来源
Advances in Computational Mathematics | 2017年 / 43卷
关键词
Superconvergence; Immersed finite element method; Interface problems; Generalized orthogonal polynomials; 65N30; 65N15; 35R05;
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学科分类号
摘要
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite element methods disappears unless the discontinuity of the coefficient is resolved by partition. We show that immersed finite element solutions inherit all desired superconvergence properties from standard finite element methods without requiring the mesh to be aligned with the interface. In particular, on interface elements, superconvergence occurs at roots of generalized orthogonal polynomials that satisfy both orthogonality and interface jump conditions.
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页码:795 / 821
页数:26
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