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Second Order Convergence of the Interpolation based on -Element

Part of: Equations of mathematical physics and other areas of application Partial differential equations, boundary value problems

Published online by Cambridge University Press:  17 November 2016

Ruijian He  and
Xinlong Feng
Ruijian He*
Affiliation:
Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, CanadaT2N 1N4
Xinlong Feng*
Affiliation:
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P. R. China
*
*Corresponding author. Email addresses:[email protected] (R.-J. He), [email protected] (X.-L. Feng)
*Corresponding author. Email addresses:[email protected] (R.-J. He), [email protected] (X.-L. Feng)
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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.

Keywords

-finite elementTensor-product polynomial spaceIntegral averageNon-uniform meshInterpolation error

MSC classification

Secondary: 35Q30: Navier-Stokes equations 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 4 , November 2016 , pp. 595 - 618
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Ciarlet, P. G., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam (1978).Google Scholar
[2] Brenner, S. C. and Scott, L. R., The Mathematical Theory of Finite Element Methods, Vol. 15. Springer, 2008.CrossRefGoogle Scholar
[3] Alexandre, Ern. and Guermond, J., Theory and Practice of Finite Elements, Vol. 159. Springer, 2004.Google Scholar
[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):154–170.Google Scholar
[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):5439–5455.CrossRefGoogle Scholar