@article{Jia_Wang_Liu_Li_2024, title={Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation}, volume={5}, url={https://ojs.wiserpub.com/index.php/CM/article/view/4041}, DOI={10.37256/cm.5220244041}, abstractNote={<p>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 <em>t<sub>n − θ</sub></em> is approximated utilizing a second-order SCQ formula, where <em>θ</em> 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.</p>}, number={2}, journal={Contemporary Mathematics}, author={Jia, Jingwei and Wang, Nian and Liu, Yang and Li, Hong}, year={2024}, month={Apr.}, pages={1164–1180} }