@Article{IJNAM-22-2,
author = {Riya, Jain and Yadav, Sangita},
title = {Hybridizable Discontinuous Galerkin Method for Linear Hyperbolic Integro-Differential Equations },
journal = {International Journal of Numerical Analysis and Modeling},
year = {2025},
volume = {22},
number = {2},
pages = {202--225},
abstract = {<p style="text-align: justify;">This article introduces the hybridizable discontinuous Galerkin (HDG) approach to
numerically approximate the solution of a linear hyperbolic integro-differential equation. A priori
error estimates for semi-discrete and fully discrete schemes are developed. It is shown that the
optimal order of convergence is achieved for both scalar and flux variables. To achieve that,
an intermediate projection is introduced for the semi-discrete error analysis, and it also shows
that this projection achieves convergence of order $h^{k+3/2}$ for $k ≥ 1.$ Next, superconvergence is
achieved for the scalar variable using element-by-element post-processing. For the fully discrete
error analysis, the central difference scheme and the mid-point rule approximate the derivative
and the integral term, respectively. Hence, the second order of convergence is achieved in the
temporal direction. Finally, numerical experiments have been performed to validate the theory
developed in this article.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2025-1010},
url = {https://global-sci.com/article/91646/hybridizable-discontinuous-galerkin-method-for-linear-hyperbolic-integro-differential-equations}
}