Convergence analysis of expanded mixed virtual element methods for nonlocal problems

Abstract

AbstractIn this article, we have developed the mixed virtual element formulation for the nonlocal parabolic problem. A priori error estimates for the semi‐discrete and the fully‐discrete schemes are derived and analyzed. The spatial discretization is based on the mixed virtual element framework, and the backward Euler method is used for the time discretization. Using Brouwer's fixed point argument, we have proved the existence and uniqueness of a fully‐discrete scheme. A set of representative numerical examples investigates such theoretical results.