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

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  • Wang, Lu
  • Feng, Minfu

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.

Suggested Citation

  • Wang, Lu & Feng, Minfu, 2025. "On the hybridizable discontinuous Galerkin method and superconvergence analysis for the diffusive viscous wave equation," Applied Mathematics and Computation, Elsevier, vol. 501(C).
    • Handle: RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325001973
    DOI: 10.1016/j.amc.2025.129471
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