A Conforming Virtual Element Method for Parabolic Integro-Differential Equations

Abstract

This article develops and analyses a conforming virtual element scheme for the spatial discretization of parabolic integro-differential equations combined with backward Euler’s scheme for temporal discretization. With the help of Ritz–Voltera and L 2 L^{2} projection operators, optimal a priori error estimates are established. Moreover, several numerical experiments are presented to confirm the computational efficiency of the proposed scheme and validate the theoretical findings.