A Residual A Posteriori error estimate for the Virtual Element Method

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 behaviour of the ratio between the error and the error estimator, resulting independent of the meshsize and element distortion.