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
收藏
页码：497 / 513
页数：17
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