Second-order BDF ADI Galerkin finite element method for the evolutionary equation with a nonlocal term in three-dimensional space

被引：34

作者：

Yang, Xuehua ^{[1
]}

Qiu, Wenlin ^{[2
]}

Chen, Haifan ^{[2
]}

Zhang, Haixiang ^{[1
]}

机构：

[1] Hunan Univ Technol, Sch Sci, Zhuzhou 412007, Hunan, Peoples R China

[2] Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Hunan, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2022年 / 172卷

基金：

中国国家自然科学基金;

关键词：

Three-dimensional nonlocal evolution equation; BDF2 ADI Galerkin method; Second-order convolution quadrature rule; Stability and convergence; Numerical experiments; PARABOLIC INTEGRODIFFERENTIAL EQUATION; IMPLICIT DIFFERENCE SCHEME; SPLINE COLLOCATION METHODS; WEAKLY SINGULAR KERNEL; NUMERICAL-SOLUTION; TIME; DIFFUSION; DISCRETIZATION;

D O I：

10.1016/j.apnum.2021.11.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we propose and analyze a new method for the solution of the three-dimensional evolutionary equation with a nonlocal term. Then the method combines Galerkin finite element methods (FEMs) for the spatial discretization with an alternating direction implicit (ADI) algorithm based on the second-order backward differentiation formula (BDF2), where the Riemann-Liouville (R-L) integral term is approximated via second-order convolution quadrature (CQ) rule. The L-2-norm stability and convergence are proved. Numerical results confirm the predicted space-time convergence rates. (C) 2021 Published by Elsevier B.V. on behalf of IMACS.

引用

页码：497 / 513

页数：17

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