Weak Galerkin methods for elliptic interface problems on curved polygonal partitions

被引：3

作者：

Li, Dan ^{[1
]}

Wang, Chunmei ^{[2
]}

Zhang, Shangyou ^{[3
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Jiangsu Key Lab NSLSCS, Nanjing 210023, Peoples R China

[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA

[3] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 150卷

基金：

美国国家科学基金会; 中国国家自然科学基金; 中国博士后科学基金;

关键词：

Weak Galerkin; Finite element methods; Elliptic interface problems; Weak gradient; Polygonal partitions; Curved elements; FINITE-ELEMENT-METHOD; MATCHED INTERFACE; EQUATIONS; CONVERGENCE;

D O I：

10.1016/j.cam.2024.115995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new weak Galerkin (WG) method for elliptic interface problems on general curved polygonal partitions. The method's key innovation lies in its ability to transform the complex interface jump condition into a more manageable Dirichlet boundary condition, simplifying the theoretical analysis significantly. The numerical scheme is designed by using locally constructed weak gradient on the curved polygonal partitions. We establish error estimates of optimal order for the numerical approximation in both discrete H-1 and H-2 norms. Additionally, we present various numerical results that serve to illustrate the robust numerical performance of the proposed WG interface method.

引用

页数：15

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