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Title: | Hdg method for linear parabolic integro-differential equations |
Authors: | Yadav, Sangita |
Keywords: | Mathematics Parabolic integro-differential equations HDG method Extended ritz-volterra projection Optimal error estimates |
Issue Date: | Aug-2023 |
Publisher: | Elsevier |
Abstract: | This paper develops the hybridizable discontinuous Galerkin (HDG) method for a linear parabolic integro-differential equation and analyzes uniform in time error bounds. To handle the integral term, an extended Ritz-Volterra projection is introduced, which helps in achieving optimal order convergence of for the semi-discrete problem when polynomials of degree 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 for . 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. |
URI: | https://www.sciencedirect.com/science/article/pii/S009630032300156X http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17643 |
Appears in Collections: | Department of Mathematics |
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