Accuracy Raising Technique for Multivariate Spline Quasi-Interpolants over Type-2 Triangulations  

作　　者：Shenggang ZHANG Chungang ZHU Qinjiao GAO 

机构地区：[1]School of Science,Zhejiang University of Science and Technology,Zhejiang 310023,P.R.China [2]School of Mathematical Sciences,Dalian University of Technology,Liaoning 116024,P.R.China [3]School of Statistics and Mathematics,Zhejiang Gongshang University,Zhejiang 310018,P.R.China [4]Collaborative Innovation Center of Statistical Data Engineering,Technology&Application,Zhejiang Gongshang University,Zhejiang 310018,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2022年第3期318-330,共13页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.12071057;11671068;12001487);the Characteristic&Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang University-Statistics)。

摘　　要：Given a multivariate quasi-interpolation operator with the partition of unity property,we propose a method to raise the accuracy with simple knots.The resulting operators possess higher accuracy while not requiring any derivative information of the underlying function.On that basis,we improve the multivariate spline quasi-interpolants with higher accuracy over type-2triangulations.Moreover,we apply the improved quasi-interpolants to simulate time developing partial differential equations(PDEs).The numerical experiments verify the efficiency of the proposed methods.

关 键 词：QUASI-INTERPOLATION polynomial reproduction multivariate spline numerical solution 

分 类 号：O241.3[理学—计算数学]