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HDG method for linear parabolic integro-Differential equations

Author

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  • Jain, Riya
  • Pani, Amiya K.
  • Yadav, Sangita

Abstract

This paper develops the hybridizable discontinuous Galerkin (HDG) method for a linear parabolic integro-differential equation and analyzes uniform in time apriori error bounds. To handle the integral term, an extended Ritz-Volterra projection is introduced, which helps in achieving optimal order convergence of O(hk+1) for the semi-discrete problem when polynomials of degree k≥0 are used to approximate both the solution and the flux variables. Further, element-by-element post-processing is proposed, and it is established that it achieves convergence of the order O(hk+2) for k≥1. Using the backward Euler method in temporal direction and quadrature rule to discretize the integral term, a fully discrete scheme is derived along with its error estimates. Finally, with the help of numerical examples in two-dimensional domains, computational results are obtained, which verify our results.

Suggested Citation

  • Jain, Riya & Pani, Amiya K. & Yadav, Sangita, 2023. "HDG method for linear parabolic integro-Differential equations," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s009630032300156x
    DOI: 10.1016/j.amc.2023.127987
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    References listed on IDEAS

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    1. B. Deka & R. C. Deka, 2013. "Finite element method for a class of parabolic integro-differential equations with interfaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(6), pages 823-847, December.
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