ON THE ACCURACY OF FINITE ELEMENT APPROXIMATIONS TO A CLASS OF INTERFACE PROBLEMS

被引：30

作者：

Guzman, Johnny ^{[1
]}

Sanchez, Manuel A. ^{[1
]}

Sarkis, Marcus ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[2] Worcester Polytech Inst, Dept Math Sci, 100 Inst Rd, Worcester, MA 01609 USA

来源：

MATHEMATICS OF COMPUTATION | 2016年 / 85卷 / 301期

基金：

美国国家科学基金会;

关键词：

Interface problems; finite elements; pointwise estimates; IMMERSED BOUNDARY METHOD; IRREGULAR REGIONS; BIHARMONIC-EQUATIONS; CONVERGENCE; FORMULATION; POISSONS; FLOW;

D O I：

10.1090/mcom3051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define piecewise linear and continuous finite element methods for a class of interface problems in two dimensions. Correction terms are added to the right-hand side of the natural method to render it second-order accurate. We prove that the method is second-order accurate on general quasi-uniform meshes at the nodal points. Finally, we show that the natural method, although non-optimal near the interface, is optimal for points O(root h log(1/h)) away from the interface.

引用

页码：2071 / 2098

页数：28

共 32 条

[1]

Adjerid S, 2014, INT J NUMER ANAL MOD, V11, P541

[2] A robust Nitsche's formulation for interface problems [J].