发表机构
Department of Mathematics and Statistics, Air Force Institute of Technology（数学与统计系，空军理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对物理科学计算中不可或缺的求积公式，提出三角化多边形区域上的通用超收敛结果，即对固定偶次二元多项式精确的求积规则，节点间距减小时可实现额外阶数收敛。
AI 中文摘要
求积公式是将定积分近似为一组函数值的线性组合，在物理科学的计算方法中普遍存在且必不可少。本文针对多边形区域上的求积公式，提出一项超收敛结果：对所有固定偶次二元多项式精确的求积规则，在节点间距减小的情况下可实现额外阶数的收敛。
英文摘要
Cubature rules, which approximate definite integrals as a linear combination of a set of function values, are ubiquitous and necessary for computational methods in the physical sciences. A superconvergence result for cubature rules on polytopal domains in two and three dimensions is developed, whereby a rule that is exact for all bivariate polynomials of a fixed even degree realizes an extra order of convergence under a decrease in the spacing between nodes.
CommentsThis work updates and corrects the proof of a previous version, while extending the result to three dimensions
