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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:hejian010@gmail.com (R.-J. He), fxlmath@xju.edu.cn (X.-L. Feng)
*Corresponding author. Email addresses:hejian010@gmail.com (R.-J. He), fxlmath@xju.edu.cn (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

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