Year: 2024
Author: Meghana Suthar, Sangita Yadav
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 504–527
Abstract
This article develops and analyses a mixed virtual element scheme for the spatial discretization of linear parabolic integro-differential equations (PIDEs) combined with backward Euler’s temporal discretization approach. The introduction of mixed Ritz-Volterra projection significantly helps in managing the integral terms, yielding optimal convergence of order $O(h^{k+1})$ for the two unknowns $p(x, t)$ and $\sigma(x, t).$ In addition, a step-by-step analysis is proposed for the super convergence of the discrete solution of order $O(h^{k+2}).$ The fully discrete case has also been analyzed and discussed to achieve $O(\tau)$ in time. Several computational experiments are discussed to validate the proposed schemes computational efficiency and support the theoretical conclusions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1020
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 4 : pp. 504–527
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Mixed virtual element method parabolic integro-differential equation error estimates super-convergence.