In the original virtual element space with degree of accuracy k, projector operators in the H1-seminorm onto polynomials of degree ≤k can be easily computed. On the other hand, projections in the L2 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 L2 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 L2 error estimates. © 2013 Elsevier Ltd. All rights reserved.
Ahmad, B., Alsaedi, A., Brezzi, F., Marini, L., Russo, A. (2013). Equivalent projectors for virtual element methods. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 66(3), 376-391 [10.1016/j.camwa.2013.05.015].
Equivalent projectors for virtual element methods
RUSSO, ALESSANDRO
2013
Abstract
In the original virtual element space with degree of accuracy k, projector operators in the H1-seminorm onto polynomials of degree ≤k can be easily computed. On the other hand, projections in the L2 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 L2 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 L2 error estimates. © 2013 Elsevier Ltd. All rights reserved.
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