Science in China Series A: Mathematics

, Volume 47, Issue 6, pp 940–949 | Cite as

New construction and ultraconvergence of derivative recovery operator for odd-degree rectangular elements

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Abstract

In this paper the ultra convergence of the derivative for odd-degree rectangular elements is addressed. A new, discrete least-squares patch recovery technique is proposed to postprocess the solution derivatives. Such recovered derivatives are shown to possess ultra convergence by using projection type interpolation.

Keywords

SPR derivative recovery operator projection type interpolation ultraconvergence 

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References

  1. 1.
    Zienkiewicz, O. C., Zhu, J. Z., The superconvergence patch recovery and a posteriori estimates. Part 1: The recovery technique, Int. J. Numer. Methods Engrg., 1992, 33: 1331–1364.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Zienkiewicz, O. C., Zhu, J. Z., The superconvergence patch recovery and a posteriori estimates. Part 2: Error estimates and adaptivity, Int. J. Numer. Methods Engrg., 1992, 33: 1365–1382.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Zienkiewicz, O. C., Zhu, J. Z., The superconvergence patch recovery (SPR) and adaptive finite element refinement, Comput. Methods Appl. Mech. Engrg., 1992, 101: 207–224.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Zienkiewicz, O. C., Zhu, J. Z., Superconvergence and the superconvergent patch recovery, Finite ELEM Anal. Des., 1995, 19: 11–23.MATHCrossRefGoogle Scholar
  5. 5.
    Zienkiewiz, O. C, Zhu, J. Z., Wu, J., Superconvergence patch recovery techniques—some further tests, Commun. Num. Math. Meth. Erg., 1993, 9: 251–258.CrossRefGoogle Scholar
  6. 6.
    Zhang, Z. M., Ultraconvergence of the patch recovery technique, Math. Comp., 1996, 65(216): 1431–1437.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Zhang, Z. M., Ultraconvergence of the patch recovery technique II, Math. Comp., 2000, 69: 141–158.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Zhang, Z. M., Zhu, J. Z., Analysis of the superconvergence patch recovery techniques and a posteriori error estimator in the finite element method (I), Comput. Methods Appl. Mech. Engrg., 1995, 123: 173–187.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Zhang, Z. M., Zhu, J. Z., Analysis of the supencorvergent patch recovery technique and a posteriori error estimator in the finite element method (II), Comput. Methods Appl. Mech. Engrg., 1998, 163: 159–170.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Zhang, Z. M., Victorg, Jr. H. D., Mathematical analysis of Zienkiewicz-zhu’s derivative patch recovery technique, Numer. Methods for PDEs, 1996, 12: 507–524.MATHGoogle Scholar
  11. 11.
    Zhu, Q. D., Zhao, Q. H., SPR technique and finite element correction, Numer. Math., 2003, 96: 185–196.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Lin, Q., Zhu, Q. D., The Preprocessing and Postprocessing for the Finite Element Method (in Chinese), Shanghai: Scientific and Technical Publishers, 1994, 7–109.Google Scholar
  13. 13.
    Wahlbin, L. B., Superconvergence in Galerkin Finite Element Methods, Lecture Notes in Mathematics 1605, New York: Springer-Verlag, 1995, 1–166.Google Scholar
  14. 14.
    Zhang, T., The derivative patch interpolating recovery technique and superconvergence, Mahematca Numerica Sinica, 2001, 23(1): 1–8.MATHGoogle Scholar
  15. 15.
    Zhu, Q. D., Natural inner superconvergence for the finite element method, in: Feng, K. and Lions, J. L. eds., Proceedings of the China-France Symposium on Finite Element Methods, Beijing: Science Press, 1983, 935–960.Google Scholar
  16. 16.
    Zhu, Q. D., Lin Q., The Superconvergence Theory of Finite Element Methods (in Chinese), Changsha: Hunan Scientific and Technical Publishers, 1989, 92–135.Google Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.College of Mathematics and Computer ScienceHunan Normal UniversityChangshaChina

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