Nitsche-XFEM for a time fractional diffusion interface problem

被引：0

作者：

Wang, Tao ^{[1
]}

Chen, Yanping ^{[2
]}

机构：

[1] China Nucl Power Technol Res Inst Co Ltd, Shenzhen 518028, Peoples R China

[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2024年 / 67卷 / 03期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

fractional diffusion; interface; discontinuous Galerkin; Nitsche-XFEM; error estimates; FINITE-ELEMENT-METHOD; EVOLUTION EQUATION; GALERKIN METHOD; SPECTRAL METHOD; CONVERGENCE; SCHEME; DISCRETIZATION; APPROXIMATIONS; REGULARITY;

D O I：

10.1007/s11425-021-2062-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a space-time finite element method for a time fractional diffusion interface problem. This method uses the low-order discontinuous Galerkin (DG) method and the Nitsche extended finite element method (Nitsche-XFEM) for temporal and spatial discretization, respectively. Sharp pointwise-in-time error estimates in graded temporal grids are derived, without any smoothness assumptions on the solution. Finally, three numerical examples are provided to verify the theoretical results.

引用

页码：665 / 682

页数：18

共 53 条

[1] FINITE ELEMENT METHOD FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS [J].

BABUSKA, I .

COMPUTING, 1970, 5 (03) :207-&

[2] Strongly stable generalized finite element method: Application to interface problems [J].

Babuska, Ivo ;

Banerjee, Uday ;

Kergrene, Kenan .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2017, 327 :58-92

[3] A finite element method for interface problems in domains with smooth boundaries and interfaces [J].

Bramble, JH ;

King, JT .

ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 6 (02) :109-138

[4] CutFEM: Discretizing geometry and partial differential equations [J].

Burman, Erik ;

Claus, Susanne ;

Hansbo, Peter ;

Larson, Mats G. ;

Massing, Andre .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2015, 104 (07) :472-501

[5] DISCONTINUOUS FINITE ELEMENT METHODS FOR INTERFACE PROBLEMS: ROBUST A PRIORI AND A POSTERIORI ERROR ESTIMATES [J].

Cai, Zhiqiang ;

He, Cuiyu ;

Zhang, Shun .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (01) :400-418

[6] GENERALIZED JACOBI FUNCTIONS AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS [J].

Chen, Sheng ;

Shen, Jie ;

Wang, Li-Lian .

MATHEMATICS OF COMPUTATION, 2016, 85 (300) :1603-1638

[7] Finite element methods and their convergence for elliptic and parabolic interface problems [J].

Chen, ZM ;

Zou, J .

NUMERISCHE MATHEMATIK, 1998, 79 (02) :175-202

[8] A hybridizable discontinuous Galerkin method for fractional diffusion problems [J].

Cockburn, Bernardo ;

Mustapha, Kassem .

NUMERISCHE MATHEMATIK, 2015, 130 (02) :293-314

[9] Convolution quadrature time discretization of fractional diffusion-wave equations [J].

Cuesta, E ;

Lubich, C ;

Palencia, C .

MATHEMATICS OF COMPUTATION, 2006, 75 (254) :673-696

[10] Numerical approximation of an interface problem for fractional in time diffusion equation [J].

Delic, Aleksandra ;

Jovanovic, Bogko S. .

APPLIED MATHEMATICS AND COMPUTATION, 2014, 229 :467-479

← 1 2 3 4 5 6 →