A Priori Error Estimates for Some Discontinuous Galerkin Immersed Finite Element Methods

被引：38

作者：

Lin, Tao ^{[1
]}

Yang, Qing ^{[2
]}

Zhang, Xu ^{[3
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] Shandong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

[3] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2015年 / 65卷 / 03期

基金：

美国国家科学基金会;

关键词：

Immersed finite element; Discontinuous Galerkin; Cartesian mesh; Interface problems; Local mesh refinement; INTERFACE PROBLEMS; INTERIOR PENALTY; ELLIPTIC PROBLEMS; EQUATIONS; DOMAINS; SPACE;

D O I：

10.1007/s10915-015-9989-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a priori error estimates for a class of interior penalty discontinuous Galerkin (DG) methods using immersed finite element (IFE) functions for a classic second-order elliptic interface problem. The error estimation shows that these methods can converge optimally in a mesh-dependent energy norm. The combination of IFEs and DG formulation in these methods allows local mesh refinement in the Cartesian mesh structure for interface problems. Numerical results are provided to demonstrate the convergence and local mesh refinement features of these DG-IFE methods.

引用

页码：875 / 894

页数：20

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