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

Authors

• Jingwei Jia School of Mathematical Sciences, Inner Mongolia University, Hohhot, China
• Nian Wang School of Mathematical Sciences, Inner Mongolia University, Hohhot, China
• Yang Liu School of Mathematical Sciences, Inner Mongolia University, Hohhot, China https://orcid.org/0000-0001-8218-0196
• Hong Li School of Mathematical Sciences, Inner Mongolia University, Hohhot, China

Keywords:

Fractional Klein-Gordon equation, SCQ scheme, spatial two-grid finite element method

Abstract

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 tn − θ is approximated utilizing a second-order SCQ formula, where θ 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.

2024-04-08

How to Cite

1.
Jia J, Wang N, Liu Y, Li H. Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation. Contemp. Math. [Internet]. 2024 Apr. 8 [cited 2024 Sep. 12];5(2):1164-80. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4041

Research Article