Superconvergent P1 honeycomb virtual elements and lifted P3 solutions.

When solving the Poisson equation on honeycomb hexagonal grids, we show that the P 1 virtual element is three-order superconvergent in H 1 -norm, and two-order superconvergent in L 2 and L ∞ norms. We define a local post-process which lifts the superconvergent P 1 solution to a P 3 solution of the optimal-order approximation. The theory is confirmed by a numerical test. [ABSTRACT FROM AUTHOR]