Hybridizable Discontinuous Galerkin Method for Linear Hyperbolic Integro-Differential Equations
Year: 2025
Author: Riya Jain, Sangita Yadav
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 202–225
Abstract
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 hk+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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2025-1010
International Journal of Numerical Analysis and Modeling, Vol. 22 (2025), Iss. 2 : pp. 202–225
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Hyperbolic integro-differential equation hybridizable discontinuous Galerkin method Ritz-Volterra projection a priori error bounds post-processing.
Author Details
Riya Jain Email
Sangita Yadav Email