This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data bounded weighted essentially non-oscillatory (WENO) approximations. Computational results show that data bounded WENO approximations for smooth functions achieve required accuracy and do not exhibit overshoot or undershoot for functions with discontinuities and extrema. Further with suitable weights, high order data-bounded WENO approximations are proposed for WENO schemes.

翻译：这项工作通过减少三等多面近似线上受数据约束的条件,对三等和四等数据结构的顺序WENO加权作了定性。使用这些条件,对三等和四等数据界定了非线性加权数,加权数基本上非循环(WENO)近似值。计算结果显示,光滑功能中受WENO约束的数据近似值达到要求的准确性,且不显示不连续和外差功能的过度或低射线。此外,还提议为WENO计划设定高等、有数据约束的WENO近似值。