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Second Order Convergence of the Interpolation based on -Element

  • Ruijian He (a1) and Xinlong Feng (a2)


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.


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*Corresponding author. Email addresses: (R.-J. He), (X.-L. Feng)


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[1] Ciarlet, P. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).
[2] Brenner, S. C. and Scott, L. R., The Mathematical Theory of Finite Element Methods, Vol. 15. Springer, 2008.
[3] Alexandre, Ern. and Guermond, J., Theory and Practice of Finite Elements, Vol. 159. Springer, 2004.
[4] He, Y. and Feng, X., H1-Stability and convergence of the FE, FV and FD methods for an elliptic equation, East Asian Journal on Applied Mathematics, 2013, 3(2):154170.
[5] Feng, X. and He, Y., H1-Super-convergence of center finite difference method based on P1-element for the elliptic equation, Applied Mathematical Modelling, 2014, 38(23):54395455.


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Second Order Convergence of the Interpolation based on -Element

  • Ruijian He (a1) and Xinlong Feng (a2)


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