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 <= k can be easily computed. On the other hand, projections in the L-2 norm are available only on polynomials of degree <= 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 L-2 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-2 error estimates. (C) 2013 Elsevier Ltd. All rights reserved.