TY - JOUR
T1 - Mixed Virtual Element Method for Linear Parabolic Integro-Differential Equations
AU - Suthar , Meghana
AU - Yadav , Sangita
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 504
EP - 527
PY - 2024
DA - 2024/06
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1020
UR - https://global-sci.org/intro/article_detail/ijnam/23200.html
KW - Mixed virtual element method, parabolic integro-differential equation, error estimates, super-convergence.
AB - <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>