Explicit Gaussian Quadrature Rules for C1 Cubic Splines with Non-uniform Knot Sequences

作     者：Peng Chen Xin Li 

作者机构：School of Mathematical SciencesUniversity of Science and Technology of ChinaHefei 230026People’s Republic of China 

出 版 物：《Communications in Mathematics and Statistics》 (数学与统计通讯（英文）)

年 卷 期：2021年第9卷第3期

页      面：331-345页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 070101[理学-基础数学] 

基　　金：The authors are supported by the NSF of China(No.61872328) NKBRPC(2011CB302400) SRF for ROCS SE and the Youth Innovation Promotion Association CAS 

主　　题：Gaussian quadrature Non-uniform Isogeometric analysis Cubic splines 

摘      要：This paper provides the explicit and optimal quadrature rules for the cubic C1 spline space,which is the extension of the results in Ait-Haddou et al.(J Comput Appl Math 290:543–552,2015)for less restricted non-uniform knot *** rules are optimal in the sense that there exist no other quadrature rules with fewer quadrature points to exactly integrate the functions in the given spline *** explicit means that the quadrature nodes and weights are derived via an explicit recursive *** experiments and the error estimations of the quadrature rules are also presented in the end.