A residual a posteriori error estimate for the Virtual Element Method

Abstract

A residual-based a posteriori error estimate for the Poisson problem with discontinuous diffusivity coefficient is derived in the case of a virtual element discretization. The error is measured considering a suitable polynomial projection of the discrete solution to prove an equivalence between the defined error and a computable residual based error estimator that does not involve any term related to the virtual element stabilization. Numerical results display a very good behavior of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.