Fast Two-Grid Finite Element Algorithm for a Fractional Klein-Gordon Equation

被引：0
作者：
Jia, Jingwei [1 ,2 ]
Wang, Nian [1 ]
Liu, Yang [1 ]
Li, Hong [1 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot, Peoples R China
[2] Katholieke Univ Leuven, Dept Math, Leuven, Belgium
来源：
CONTEMPORARY MATHEMATICS | 2024年 / 5卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Fractional Klein-Gordon equation; SCQ scheme; spatial two-grid finite element method; NUMERICAL-SIMULATION; SINE-GORDON; DIFFUSION; SCHEME;
D O I：
10.37256/cm.5220244041
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we propose a spatial two-grid finite element algorithm combined with a shifted convolution quadrature (SCQ) formula for solving the fractional Klein-Gordon equation. The time direction at t(n -) (theta) . is approximated utilizing a second-order SCQ formula, where theta is an arbitrary constant. The spatial discretization is performed using a two-grid finite element method involving three steps: calculating the numerical solution by solving a nonlinear system iteratively on the coarse grid, obtaining the interpolation solution based on the computed solutions in the first step, and solving a linear finite element system on the fine grid. We present a numerical algorithm, validate the two-grid finite element method's effectiveness, and demonstrate the computational efficiency for our method by the comparison of the computing results between the two-grid finite element method and the standard finite element method.
引用
收藏
页码：1294 / 1310
页数：17
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