HDG method for linear parabolic integro-Differential equations

Riya Jain, Amiya K. Pani and Sangita Yadav

Applied Mathematics and Computation, 2023, vol. 450, issue C

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.

Keywords: Parabolic integro-differential equation; HDG Method; Extended Ritz-Volterra projection; Optimal error estimates; Super-convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:450:y:2023:i:c:s009630032300156x

DOI: 10.1016/j.amc.2023.127987

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