Equivalent projectors for Virtual Element Methods

In the original Virtual Element space with degree of accuracy k, projector operators in the H^1-seminorm onto polynomials of degree smaller than or equal to k can be easily computed. On the other hand, projections in the L^2 norm are available only on polynomials of degree smaller than or equal to k-2 (directly from the degrees of freedom). Here we present a variant of VEM that allows the exact computations of the L^2 projections on all polynomials of degree up to 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^2 error estimates.