Equivalent projectors for virtual element methods

In the original Virtual Element space with degree of accuracy k, projector operators in theH-seminorm onto polynomials of degree ≤ k can be easily computed. On the other hand, projections in the L norm are available only on polynomials of degree ≤ k − 2 (directly from the degrees of freedom). Here we present a variant of VEM that allows the exact computations of the L projections on all polynomials of degree ≤ k. The interest of this construction is illustrated with some simple examples, including the construction of three-dimensional Virtual Elements, the treatment of lower order terms, the treatment of the right-hand side, and the L error estimates.