On the Approximation of the Derivatives of Spline Quasi-Interpolation in Cubic Spline Space S_(3)^(1,2)(∆_(mn)^((2)))  

作　　者：Jiang Qian Fan Wang 

机构地区：[1]College of Sciences,Hohai University,Nanjing 210098,China [2]Center for Numerical Simulation Software in Engineering and Sciences,Department of Engineering Mechanics,Hohai University,Nanjing 210098,China [3]College of Engineering,Nanjing Agricultural University,Nanjing 210031,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2014年第1期1-22,共22页高等学校计算数学学报（英文版）

基　　金：The authors wish to express our great appreciation to Prof.Renhong Wang for his valuable suggestions.Also,the authors would like to thank Dr.Chongjun Li and Dr.Chungang Zhu for their help;This work is supported by National Basic Research Program of China(973 Project No.2010CB832702);R and D Special Fund for Public Welfare Industry(Hydrodynamics,Grant No.201101014);National Science Funds for Distinguished Young Scholars(Grant No.11125208);Programme of Introducing Talents of Discipline to Universities(111 project,Grant No.B12032);This work is supported by the Fundamental Research Funds for the Central Universities,and Hohai University Postdoctoral Science Foundation 2016-412051.

摘　　要：In this paper,based on the basis composed of two sets of splines with distinct local supports,cubic spline quasi-interpolating operators are reviewed on nonuniform type-2 triangulation.The variation diminishing operator is defined by discrete linear functionals based on a fixed number of triangular mesh-points,which can reproduce any polynomial of nearly best degrees.And by means of the modulus of continuity,the estimation of the operator approximating a real sufficiently smooth function is reviewed as well.Moreover,the derivatives of the nearly optimal variation diminishing operator can approximate that of the real sufficiently smooth function uniformly over quasi-uniform type-2 triangulation.And then the convergence results are worked out.

关 键 词：Bivariate splines conformality of smoothing cofactor method nonuniform type-2 triangulation QUASI-INTERPOLATION modulus of continuity 

分 类 号：O17[理学—数学]