On the hybridizable discontinuous Galerkin method and superconvergence analysis for the diffusive viscous wave equation

Lu Wang and Minfu Feng

Applied Mathematics and Computation, 2025, vol. 501, issue C

Abstract: This paper studies the hybridizable discontinuous Galerkin (HDG) method for solving the diffusive viscous wave equation. We provide a theoretical analysis of both the semi-discrete and fully-discrete schemes. Our results demonstrate that the displacement and the flux converge with an order of m+1 in the L2 norm where m is the degree of polynomials. We also present a superconvergence analysis, indicating that the local post-processed variable converges with an order of m+2 in the L2 norm. Finally, numerical tests verify our analysis.

Keywords: Diffusive-viscous wave equation; Hybridizable discontinuous Galerkin; Semi-discrete scheme; Fully-discrete scheme; Superconvergence (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325001973

DOI: 10.1016/j.amc.2025.129471

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