CONSTRUCTION OF CUBATURE FORMULAS VIA BIVARIATE QUADRATIC SPLINE SPACES OVER NON-UNIFORM TYPE-2 TRIANGULATION  

作　　者：Jiang Qian Xiquan Shi Jinming Wu Dianxuan Gong 

机构地区：[1]College of Science,Hohai University,Nanjing 211100,China [2]Key Laboratory of Coastal Disaster and Defence(Hohai University),Ministry of Education,Nanjing 210098,China [3]Division of Physics,Engineering,Mathematics,and Computer Science,Delaware State University,Dover,DE 19901,USA [4]Statistics and Mathematics Institute,Zhejiang Gongshang University,Hangzhou 310018,China [5]College of Science,North China University of Science and Technology,Tangshan 063210,China

出　　处：《Journal of Computational Mathematics》2022年第2期205-230,共26页计算数学（英文）

基　　金：This work was supported by the Fundamental Research Funds for the Central Universities of Hohai University(Grant No.2019B19414,2019B44914);the Natural Science Foundation of Jiangsu Province for the Youth(Grant No.BK20160853);Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202011);the National Natural Science Foundation of China(Grant No.11601151);the National Science Foundation of Zhejiang Province(Grant No.LY19A010003).

摘　　要：In this paper,matrix representations of the best spline quasi-interpolating operator over triangular sub-domains in S_(2)^(1)(△_(mn)^(2),and coefficients of splines in terms of B-net are calculated firstly.Moreover,by means of coefficients in terms of B-net,computation of bivariate numerical cubature over triangular sub-domains with respect to variables x and y is transferred into summation of coefficients of splines in terms of B-net.Thus concise bivariate cubature formulas are constructed over rectangular sub-domain.Furthermore,by means of module of continuity and max-norms,error estimates for cubature formulas are derived over both sub-domains and the domain.

关 键 词：Multivariate spline Bivariate cubature Conformality of Smoothing Cofactor Method B-net Non-uniform Type-2 Triangulation 

分 类 号：O24[理学—计算数学]