Superconvergent P1 honeycomb virtual elements and lifted P3 solutions

期刊论文
发表日期：

2024年10月13日

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Yanping Lin,
Xuejun Xu,
Shangyou Zhang

摘要

When solving the Poisson equation on honeycomb hexagonal grids, we show that the $P_1$ $P_{1}$ virtual element is three-order superconvergent in $H^1$ $H^{1}$ -norm, and two-order superconvergent in $L^2$ $L^{2}$ and $L^\infty $ $L^{\infty}$ norms. We define a local post-process which lifts the superconvergent $P_1$ $P_{1}$ solution to a $P_3$ $P_{3}$ solution of the optimal-order approximation. The theory is confirmed by a numerical test.