Second Order Convergence of the Interpolation based on -Element. Issue 4 (17th November 2016)

• Record Type: Journal Article
• Authors: He, Ruijian; Feng, Xinlong
• Is Part Of: Numerical mathematics. Volume 9:Issue 4(2016)
• Page Start: 595
• Page End: 618
• Publication Date: 2016-11-17
• Subjects: 35Q30, -- 65N30; -finite element, -- Tensor-product polynomial space, -- Integral average, -- Non-uniform mesh, -- Interpolation error; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2016.m1503
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: In this paper, the second order convergence of the interpolation based on -element is derived in the case of d =1, 2 and 3. Using the integral average on each element, the new basis functions of tensor product type is builded up and we can easily extend it to the higher dimensional case. Finally, some numerical tests are made to show the analytical results of the interpolation errors.