Mixed virtual element method for integro-differential equations of parabolic type

Abstract

This article presents and analyzes a mixed virtual element approach for discretizing parabolic integro-differential equations in a bounded subset of , in addition to the backward Euler approach for temporal discretization. With the help of the intermediate projection along with Fortin and projections, we effectively tackle the treatment of integral terms in both the fully discrete and semi-discrete analysis. This inclusion leads to the derivation of optimal a priori error estimates with an order of for the two unknowns. Furthermore, we present a systematic analysis that outlines the step-by-step process for achieving super convergence of the discrete solution, with an order of . Several computational experiments are discussed to validate the proposed scheme’s computational efficiency and support the theoretical conclusions.