Skip to main content
SpringerLink
Log in

Convergence Analysis of Carey Nonconforming Finite Element for the Second-Order Elliptic Problem with the Lowest Regularity

  • Published:
Russian Physics Journal Aims and scope

In this paper, the Carey nonconforming finite element method (NFEM) for the second order elliptic problem is discussed. By means of the different techniques from the existing literatures, the non-uniform and uniform convergences are obtained only under the lowest regularity assumption on the solution \( u\in {H}_0^1\left(\Omega \right). \)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. F. Carey, Comput. Methods Appl. Mech. Eng., 9, 165–179 (1976).

    Article  ADS  Google Scholar 

  2. Z. C. Shi, Comput. Methods Appl. Mech. Eng., 48, 123–137 (1985).

    Article  ADS  Google Scholar 

  3. D. Y. Shi, L. F. Pei, J. Syst. Sci. & Math. Scis., 29, No. 6, 854–864 (2009).

    Google Scholar 

  4. D. Y. Shi, S. C. Shi, and I. Hagiwara, J. Comp. Math., 23, No. 4, 373–382 (2005).

    Google Scholar 

  5. D. Y. Shi, C. X. Wang, Chin. J. Engrg. Math., 23, No. 3, 399–406 (2006).

    ADS  Google Scholar 

  6. D. Y. Shi, X. B. Hao, Chin. J. Engrg. Math., 26, No. 6, 1021–1026 (2009).

    Google Scholar 

  7. D. Y. Shi, X. B. Hao, J. Syst. Sci. & Math., 21. No. 3, 456–462 (2008).

    Google Scholar 

  8. S. C. Chen, D. Y. Shi, and Y. C. Zhao, IMA J. Numer. Anal., 24. No. 1, 77–95 (2004).

    Article  MathSciNet  Google Scholar 

  9. D. Y. Shi and H. Liang, J. Appl. Math. Mech., 28, No. 1, 119–125 (2007).

    Article  MathSciNet  Google Scholar 

  10. D. Y. Shi and L. F. Pei, Appl. Math. Comp., 219, No. 17, 9447–9460 (2013).

    Article  Google Scholar 

  11. A. H. Schatz and J. P. Wang, Math. Comp., 65, 19–27 (1996).

    Article  MathSciNet  ADS  Google Scholar 

  12. L. H. Wang, J. Comput. Math., 18, No. 3, 277–282 (2000).

    MathSciNet  Google Scholar 

  13. L. H. Wang, J. Comput. Math., 17, No. 6, 609–614 (1999).

    MathSciNet  Google Scholar 

  14. P. G. Ciarlet, J. Appl. Mech., 45, No. 4, 968–969 (1978).

    Article  ADS  Google Scholar 

  15. R. Rannacher and S. Turek, Numer. Meth. Part. Differ. Equat., 8, 97–111 (1992).

    Article  Google Scholar 

  16. D. Y. Shi and C. X. Wang, Inter. J. Comput. Math., 88, No. 10, 2167–2177 (2011).

    Article  Google Scholar 

  17. D. Y. Shi, S. P. Mao, and S. C. Chen, J. Comput. Math., 23, No. 3, 261–274 (2005).

    MathSciNet  Google Scholar 

  18. D. Y. Shi, L. F. Pei, Inter. J. Numer. Anal. Model., 5, No. 3, 373–385 (2008).

    MathSciNet  Google Scholar 

  19. D. Y. Shi, H. H. Wang, and Y. D. Du, J. Comput. Math., 27, Nos. 2–3, 299–314 (2009).

    MathSciNet  Google Scholar 

  20. D. Y. Shi and J. C. Ren, Inter. J. Numer. Anal. Model., 6, No. 2, 293–310 (2009).

    Google Scholar 

  21. D. Y. Shi and J. C. Ren, Nonlinear Anal. TMA, 71, No. 9, 3842–3852 (2009).

    Article  Google Scholar 

  22. Q. Lin, T. Lutz, and A. H. Zhou, IMA J. Numer. Anal., 25, 160–181 (2005).

    Article  MathSciNet  Google Scholar 

  23. D. Y. Shi and C. H. Yao, Numer. Meth. Part. Diff. Equat., 30, No. 5, 1654–1673 (2014).

    Article  Google Scholar 

  24. J. Hu and Z. C. Shi, J. Comput. Math., 23, No. 6, 561–586 (2005).

    MathSciNet  Google Scholar 

  25. C. Park and D. Sheen, SIAM. J. Numer. Anal., 41, No. 2, 624–640 (2003).

    Article  MathSciNet  Google Scholar 

  26. A. Q. Baig, M. Naeem, and W. Gao, Appl. Math. Nonlinear Sci., 3, No. 1, 33–40 (2018).

    Article  MathSciNet  Google Scholar 

  27. M. Dewasurendra and K. Vajravelu, Appl. Math. Nonlinear Sci., 3, No. 1, 1–14 (2018).

    Article  MathSciNet  Google Scholar 

  28. P. Lakshminarayana, K. Vajravelu, G. Sucharitha, et al., Appl. Math. Nonlinear Sci., 3, No. 1, 41–54 (2018).

    Article  MathSciNet  Google Scholar 

  29. S. Aidara, Appl. Math. Nonlinear Sci., 4, No. 1, 9–20 (2019).

    Article  MathSciNet  Google Scholar 

  30. R. Amanda and A. Atangana, Chaos Solitons Fractals, 116, 414–423 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Wang, S. Du, A. Atangana, et al., Multimed. Tools Appl., 77, No. 3, 3701–3714 (2018).

    Article  Google Scholar 

  32. C. H. Yao and L. X. Wang, Numer. Math. Theory Meth. Appl., 10, No. 1, 145–166 (2017).

    Article  MathSciNet  Google Scholar 

  33. C. H. Yao and S. H. Jia, Appl. Math. Comput., 229, 34–40 (2014).

    MathSciNet  Google Scholar 

  34. Z. H. Qiao, C. H. Yao, and S. H. Jia, J. Sci. Comput., 46, No. 1, 1–19 (2011).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, China

    Dongwei Shi

  2. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China

    CaixiaWang

Authors
  1. Dongwei Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. CaixiaWang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dongwei Shi.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–56, February, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shi, D., CaixiaWang Convergence Analysis of Carey Nonconforming Finite Element for the Second-Order Elliptic Problem with the Lowest Regularity. Russ Phys J 64, 246–254 (2021). https://doi.org/10.1007/s11182-021-02322-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-021-02322-5

Keywords

Search

Navigation