A new Petrov-Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions

被引：0

作者：

Tang, Zhongliang ^{[1
]}

Zheng, Yu ^{[1
]}

Wang, Liqun ^{[2
]}

Wang, Quanxiang ^{[1
]}

机构：

[1] Nanjing Agr Univ, Coll Sci, Nanjing 210095, Peoples R China

[2] China Univ Petr, Coll Sci, Beijing 102249, Peoples R China

来源：

JOURNAL OF ENGINEERING MATHEMATICS | 2023年 / 141卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Cartesian mesh; Immersed finite element; Petrov-Galerkin; Three-dimensional interface problems; EQUATIONS; APPROXIMATION; FLOW;

D O I：

10.1007/s10665-023-10286-3

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we develop a Petrov-Galerkin immersed finite element method for solv-ing elliptic interface problems in two and three dimensions. By introducing additional immersed finite element function on interface element, the non-homogeneous jump conditions can be dealt easily. In various test cases, including large jump in the coeffi-cients and complex interfaces, the method can provide nearly second-order accuracy in the L-2 and L-8 norm.

引用

页数：24

共 30 条

[1] FITTED AND UNFITTED FINITE-ELEMENT METHODS FOR ELLIPTIC-EQUATIONS WITH SMOOTH INTERFACES
BARRETT, JW
ELLIOTT, CM
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1987, 7 (03) : 283 - 300
[2] Bernardi C, 2000, NUMER MATH, V85, P579, DOI 10.1007/s002110000135
[3] Discontinuous bubble scheme for elliptic problems with jumps in the solution
Chang, Kwang S.
Kwak, D. Y.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (5-8) : 494 - 508
[4] An interface-fitted mesh generator and virtual element methods for elliptic interface problems
Chen, Long
Wei, Huayi
Wen, Min
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 334 : 327 - 348
[5] The immersed finite volume element methods for the elliptic interface problems
Ewing, RE
Li, ZL
Lin, T
Lin, YP
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 1999, 50 (1-4) : 63 - 76
[6] The extended/generalized finite element method: An overview of the method and its applications
Fries, Thomas-Peter
Belytschko, Ted
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 84 (03) : 253 - 304
[7] An immersed finite element method for elliptic interface problems in three dimensions
Guo, Ruchi
Lin, Tao
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 414
[8] A cut finite element method for a Stokes interface problem
Hansbo, Peter
Larson, Mats G.
Zahedi, Sara
[J]. APPLIED NUMERICAL MATHEMATICS, 2014, 85 : 90 - 114
[9] A Bilinear Immersed Finite Volume Element Method for the Diffusion Equation with Discontinuous Coefficient
He, X. -M.
Lin, T.
Lin, Y.
[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2009, 6 (01) : 185 - 202
[10] The Convergence of the Bilinear and Linear Immersed Finite Element Solutions to Interface Problems
He, Xiaoming
Lin, Tao
Lin, Yanping
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (01) : 312 - 330

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