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）] 

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 values.The 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 space.The explicit means that the quadrature nodes and weights are derived via an explicit recursive formula.Numerical experiments and the error estimations of the quadrature rules are also presented in the end.