Accuracy Raising technique for multi-variate spline quasi-interpolants over type-2 triangulations
Received:May 21, 2021  Revised:June 22, 2021
Key Word: Quasi-interpolation   polynomial reproduction   multivariate spline   numerical solution  
Fund ProjectL:National Natural Science Foundation of China (No. 12071057, 11671068, 12001487); the Characteristic $\&$ Preponderant Discipline of Key Construction Universities in Zhejiang Province (Zhejiang Gongshang University- Statistics)
Author NameAffiliationAddress
Shenggang Zhang Dalian University of Technology No.2 Linggong Road, Ganjingzi District, Dalian City, Liaoning Province, P.R.C., 116024
Chungang Zhu Dalian University of Technology 
Qinjiao Gao Zhejiang Gongshang University 
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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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