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Hybridizable discontinuous Galerkin method for nonlinear hyperbolic integro-differential equations

Author

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  • Jain, Riya
  • Yadav, Sangita

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.

Suggested Citation

  • Jain, Riya & Yadav, Sangita, 2025. "Hybridizable discontinuous Galerkin method for nonlinear hyperbolic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 498(C).
    • Handle: RePEc:eee:apmaco:v:498:y:2025:i:c:s0096300325001201
    DOI: 10.1016/j.amc.2025.129393
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