@Article{IJNAM-21-4,
author = {Suthar, Meghana and Yadav, Sangita},
title = {Mixed Virtual Element Method for Linear Parabolic Integro-Differential Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {4},
pages = {504--527},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1020},
url = {https://global-sci.com/article/91067/mixed-virtual-element-method-for-linear-parabolic-integro-differential-equations}
}