TY - JOUR
AU - Jia, Jingwei
AU - Wang, Nian
AU - Liu, Yang
AU - Li, Hong
PY - 2024/04/08
Y2 - 2024/10/05
TI - Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation
JF - Contemporary Mathematics
JA - Contemp. Math.
VL - 5
IS - 2
SE - Research Article
DO - 10.37256/cm.5220244041
UR - https://ojs.wiserpub.com/index.php/CM/article/view/4041
SP - 1164-1180
AB - <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>
ER -