Equivalent projectors for virtual element methods

Authors:
B. Ahmad;A. Alsaedi;F. Brezzi;L. D. Marini;A. Russo
Affiliations:
-;-;-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

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.