 Hybridizable discontinuous Galerkin method for nonlinear hyperbolic integro-differential equationsRiya Jain and Sangita Yadav Applied Mathematics and Computation, 2025, vol. 498, issue C Abstract: In this paper, we present the hybridizable discontinuous Galerkin (HDG) method for a nonlinear hyperbolic integro-differential equation. We discuss the semi-discrete and fully-discrete error analysis of the method. For the semi-discrete error analysis, an extended type mixed Ritz-Volterra projection is introduced for the model problem. It helps to achieve the optimal order of convergence for the unknown scalar variable and its gradient. Further, a local post-processing is performed, which helps to achieve super-convergence. Subsequently, by employing the central difference scheme in the temporal direction and applying the mid-point rule for discretizing the integral term, a fully discrete scheme is formulated, accompanied by its corresponding error estimates. Ultimately, through the examination of numerical examples within two-dimensional domains, computational findings are acquired, thus validating the results of our study. Keywords: Lipschitz continuity; HDG projection; Dual problem; Central difference scheme; Mid-point rule; Post-processing; A priori error estimates (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001201 DOI: 10.1016/j.amc.2025.129393 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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