Convergence analysis of carey nonconforming finite element for the second-order elliptic problem with the lowest regularity | Izvestiya vuzov. Fizika. 2021. № 2. DOI: 10.17223/00213411/64/2/50

Convergence analysis of carey nonconforming finite element for the second-order elliptic problem with the lowest regularity

In this paper, the Carey nonconforming finite element method (NFEM) for the second order elliptic problem are discussed. By means of the different techniques from the existing literatures, the non-uniform and uniform convergence are obtained only with the lowest regularity assumption of the solution .

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Keywords

Carey nonconforming finite element, non-uniform and uniform, lowest regularity, convergence analysis and error estimates

Authors

NameOrganizationE-mail
Dongwei Shi School of Mathematical Sciences, Henan Institute of Science and Technologyshidongwei@hist.edu.cn
Caixia Wang School of Mathematics and Statistics, North China University of Water Resources and Electric Powerwangcaixia@ncwu.edu.cn
Всего: 2

References

Carey G.F. // Comput. Method. Appl. Mech. Eng. - 1976. - V. 9. - P. 165-179.
Shi Z.C. // Comput. Method. Appl. Mech. Eng. - 1985. - V. 48. - P. 123-137.
Shi D.Y. and Pei L.F. // J. Sys. Sci. Math. Sci. - 2009. - V. 29. - No. 6. - P. 854-864.
Shi D.Y., Shi S.C., and Hagiwara I. // J. Comp. Math. - 2005. - V. 23. - No. 4. - P. 373-382.
Shi D.Y. and Wang C.X. // Chin. J. Eng. Math. - 2006. - V. 23. - No. 3. - P. 399-406.
Shi D.Y. and Hao X.B. // Chin. J. Eng. Math. - 2009. - V. 26. - No. 6. - P. 1021-1026.
Shi D.Y. and Hao X.B. // J. Syst. Sci. Math. - 2008. - V. 21. - No. 3. - P. 456-462.
Chen S.C., Shi D.Y., and Zhao Y.C. // IMA J. Numer. Anal. - 2004. - V. 24. - No. 1. - P. 77-95.
Shi D.Y. and Liang H. // Appl. Math. Mech. - 2007. - V. 28. - No. 1. - P. 119-125.
Shi D.Y. and Pei L.F. // Appl. Math. Comp. - 2013. - V. 219. - No. 17. - P. 9447-9460.
Schatz A.H. and Wang J.P. // Math. Comp. - 1996. - V. 65. - P. 19-27.
Wang L.H. // J. Comput. Math. - 2000. - V. 18. - No. 3. - P. 277-282.
Wang L.H. // J. Comput. Math. - 1999. - V. 17. - No. 6. - P. 609-614.
Ciarlet P.G. // J. Appl. Mech. Dec - 1978. - V. 45. - No. 4. - P. 968-969.
Rannacher R. and Turek S. // Numer. Meth. for PDEs. - 1992. - V. 8. - P. 97-111.
Shi D.Y. and Wang C.X. // Inter. J. Comput. Math. - 2011. - V. 88. - No. 10. - P. 2167-2177.
Shi D.Y., Mao S.P., and Chen S.C. // J. Comput. Math. - 2005. - V. 23. - No. 3. - P. 261-274.
Shi D.Y. and Pei L.F. // Inter. J. Numer. Anal. Model. - 2008. - V. 5. - No. 3. - P. 373-385.
Shi D.Y., Wang H.H., and Du Y.D. // J. Comput. Math. - 2009. - V. 27. - No. 2-3. - P. 299-314.
Shi D.Y. and Ren J.C. // Inter. J. Numer. Anal. Model. - 2009. - V. 6. - No. 2. - P. 293-310.
Shi D.Y. and Ren J.C. // Nonlinear Anal. TMA. - 2009. - V. 71. - No. 9. - P. 3842-3852.
Lin Q., Lutz T., and Zhou A.H. // IMA J. Numer. Anal. - 2005. - V. 25. - P. 160-181.
Shi D.Y. and Yao C.H. // Numer. Meth. for PDEs. - 2014. - V. 30. - No. 5. - P. 1654-1673.
Hu J. and Shi Z.C. // J. Comput. Math. - 2005. - V. 23. - No. 6. - P. 561-586.
Park C. and Sheen D. // SIAM. J. Numer. Anal. - 2003. - V. 41. - No. 2. - P. 624-640.
Baig A.Q., Naeem M., and Gao W. // Appl. Math. Nonlinear. Sci. - 2018. - V. 3. - No. 1. - P. 33-40.
Dewasurendra M. and Vajravelu K. // Appl. Math. Nonlinear. Sci. - 2018. - V. 3. - No. 1. - P. 1-14.
Lakshminarayana P., Vajravelu K., Sucharitha G., et al. // Appl. Math. Nonlinear. Sci. - 2018. - V. 3. - No. 1. - P. 41-54.
Aidara S. // Appl. Math. Nonlinear Sci. - 2019. - V. 4. - No. 1. - P. 9-20.
Amanda R. and Atangana A. // Chaos Solitons Fractals. - 2018. - V. 116. - P. 414-423.
Wang S., Du S., Atangana A., et al. // Multimedia Tools Appl. - 2018. - V. 77. - No. 3. - P. 3701-3714.
Yao C.H. and Wang L.X. // Numer. Math. Theory Methods Appl. - 2017. - V. 10. - No. 1. - P. 145-166.
Yao C.H. and Jia S.H. // Appl. Math. Comput. - 2014. - V. 229. - P. 34-40.
Qiao Z.H., Yao C.H., and Jia S.H. // J. Sci. Comput. - 2011. - V. 46. - No. 1. - P. 1-19.
 Convergence analysis of carey nonconforming finite element for the second-order elliptic problem with the lowest regularity | Izvestiya vuzov. Fizika. 2021. № 2. DOI: 10.17223/00213411/64/2/50

Convergence analysis of carey nonconforming finite element for the second-order elliptic problem with the lowest regularity | Izvestiya vuzov. Fizika. 2021. № 2. DOI: 10.17223/00213411/64/2/50