Accuracy Raising Technique for Multivariate Spline Quasi-Interpolants over Type-2 Triangulations
Received:May 21, 2021  Revised:June 27, 2021
Key Words: quasi-interpolation   polynomial reproduction   multivariate spline   numerical solution  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.12071057; 11671068; 12001487) and the Characteristic \& Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University-Statistics).
Author NameAffiliation
Shenggang ZHANG School of Science, Zhejiang University of Science and Technology, Zhejiang 310023, P. R. China 
Chungang ZHU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Qinjiao GAO School of Statistics and Mathematics, Zhejiang Gongshang University, Zhejiang 310018, P. R. China
Collaborative Innovation Center of Statistical Data Engineering, Technology & Application, Zhejiang Gongshang University, Zhejiang 310018, P. R. China 
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      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-2 triangulations. 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.
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