HIGHER DEGREE IMMERSED FINITE ELEMENT METHODS FOR SECOND-ORDER ELLIPTIC INTERFACE PROBLEMS

被引：0

作者：

Adjerid, Slimane ^{[1
]}

Ben-Romdhane, Mohamed ^{[2
]}

Lin, Tao ^{[1
]}

机构：

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

[2] Gulf Univ Sci & Technol, Dept Math & Nat Sci, Kuwait 32093, Kuwait

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2014年 / 11卷 / 03期

基金：

美国国家科学基金会;

关键词：

Immersed finite element; immersed interface; interface problems; Cartesian mesh method; structured mesh; higher degree finite element; APPROXIMATION CAPABILITY; SPACE; FORMULATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present higher degree immersed finite element (IFE) spaces that can be used to solve two dimensional second order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. The interpolation errors in the proposed piecewise pth degree spaces yield optimal O(h(p+1)) and O(h(p)) convergence rates in the L-2 and broken H-1 norms, respectively, under mesh refinement. A partially penalized method is developed which also converges optimally with the proposed higher degree IFE spaces. While this penalty is not needed when either linear or bilinear IFE space is used, a numerical example is presented to show that it is necessary when a higher degree IFE space is used.

引用

页码：541 / 566

页数：26

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