Equivalent projectors for virtual element methods

In the original virtual element space with degree of accuracy kk, projector operators in the H1H1-seminorm onto polynomials of degree ≤k≤k can be easily computed. On the other hand, projections in the L2L2 norm are available only on polynomials of degree ≤k−2≤k−2 (directly from the degrees of freedom). Here, we present a variant of the virtual element method that allows the exact computations of the L2L2 projections on all polynomials of degree ≤k≤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 L2L2 error estimates.