@article{Zhao2022, 
author = {Zhengang Zhao and Yunying Zheng and Xianglin Zeng},
title = {Finite element approximation of fractional hyperbolic integro-differential equation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {8},
pages = {15348-15369},
keywords = {fractional hyperbolic integro-differential equation, fractional derivative, fractional Ritz-Volterra projection, Galerkin finite element method},
url = {https://www.sciopen.com/article/10.3934/math.2022841},
doi = {10.3934/math.2022841},
abstract = {In this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element method in spatial direction, we apply a second order symmetric difference method in time. Next we discuss the regularity analysis of the weak solution and convergence analysis of the semi-discrete scheme. Then we further study the stability analysis and the error estimation of the fully discrete problems, according to the properties of fractional Ritz-Volterra projection, Ritz projection and so on. Numerical examples with comparisons among the proposed schemes verify our theoretical analyses.}
}