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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/handle/123456789/17643
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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