A review of two different approaches for superconvergence analysis

Qiding Zhu

Applications of Mathematics (1998)

  • Volume: 43, Issue: 6, page 401-411
  • ISSN: 0862-7940

Abstract

top
In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.

How to cite

top

Zhu, Qiding. "A review of two different approaches for superconvergence analysis." Applications of Mathematics 43.6 (1998): 401-411. <http://eudml.org/doc/33019>.

@article{Zhu1998,
abstract = {In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.},
author = {Zhu, Qiding},
journal = {Applications of Mathematics},
keywords = {finite element method; superconvergence error estimates; finite element method; superconvergence error estimates},
language = {eng},
number = {6},
pages = {401-411},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A review of two different approaches for superconvergence analysis},
url = {http://eudml.org/doc/33019},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Zhu, Qiding
TI - A review of two different approaches for superconvergence analysis
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 6
SP - 401
EP - 411
AB - In 1995, Wahbin presented a method for superconvergence analysis called “Interior symmetric method,” and declared that it is universal. In this paper, we carefully examine two superconvergence techniques used by mathematicians both in China and in America. We conclude that they are essentially different.
LA - eng
KW - finite element method; superconvergence error estimates; finite element method; superconvergence error estimates
UR - http://eudml.org/doc/33019
ER -

References

top
  1. 10.1090/S0025-5718-1977-0431744-9, Math. Comp. 31 (1977), 94–111. (1977) MR0431744DOI10.1090/S0025-5718-1977-0431744-9
  2. Optimal points of the stresses approximated by triangular linear element in FEM, Natur. Sci. J. Xiangtan Univ. 1 (1978), 77–90. (1978) 
  3. Superconvergence of finite element solution and its derivatives, Numer. Math. J. Chinese Univ. 3:2 (1981), 118–125. (1981) MR0635547
  4. Superconvergence of gradient of triangular linear element in general domain, Natur. Sci. J. Xiangtan Univ. 1 (1987), 114–127. (1987) MR0899930
  5. A new estimate for the finite element method and optimal point theorem for stresses, Natur. Sci. J. Xiangtan Univ. 1 (1978), 10–20. (1978) 
  6. The finite element method for 4th order non-linear differential equation, Acta Mathematica Sinica 20:2 (1977), 109–118. (1977) MR0657978
  7. Some superconvergence results for Galerkin methods for the approximate solution of two-point boundary value problems, Topics in Numerical Analysis, Academic Press, 1973, pp. 89–92. (1973) MR0366044
  8. An L ∞ estimate and a superconvergence result for a Galerkin method for elliptic equations based on tensor products of piecewise polynomials, RAIRO Anal. Numér. 8 (1974), 61–66. (1974) MR0359358
  9. A derivative extrapolation for second order triangular element, (1997), Master thesis. (1997) 
  10. The high accuracy arithmetic for k -th order rectangular finite element, (1990), Master thesis. (1990) 
  11. 10.1007/BF00047538, Acta Appl. Math. 9 (1987), 175–198. (1987) DOI10.1007/BF00047538
  12. Superconvergence for higher-order triangular finite elements, Chinese J. Numer. Math. Appl. 12 (1990), 75–79. (1990) MR1118707
  13. Maximum norm estimates extrapolation and optimal points of stresses for the finite element methods on the strongly regular triangulation, J. Comput. Math. 1 (1983), 376–383. (1983) 
  14. Linear finite elements with high accuracy. J. Comput. Math. 3, (1985), 115–133. (1985) MR0854355
  15. Construction and Analysis for Efficient Finite Element Method, Hebei University Press, 1996. (Chinese) (1996) 
  16. Asymptotic expansion for the derivative of finite elements, J. Comput. Math. 2 (1984), 361–363. (1984) MR0869509
  17. The Preprocessing and Postprocessing for the Finite Element Method, Shanghai Scientific & Technical Publishers, 1994. (1994) 
  18. 10.1016/0041-5553(69)90159-1, U.S.S.R. Comput. Math. and Math. Phys. 9 (1969), 158–183. (1969) DOI10.1016/0041-5553(69)90159-1
  19. 10.1137/0733027, SIAM J. Numer. Anal. 33 (1996), 505–521. (1996) MR1388486DOI10.1137/0733027
  20. Interior maximum norm estimates for finite element methods, Part II., Math. Comp (1995). (1995) MR0431753
  21. 10.2307/2005998, Math. Comp. 31 (1977), 652–660. (1977) MR0438664DOI10.2307/2005998
  22. Superconvergence in Galerkin Finite Element Methods, LN in Math. 1605, Springer, Berlin, 1995. (1995) Zbl0826.65092MR1439050
  23. General principles of superconvergence in Galerkin finite element methods, In Finite element methods: superconvergence, post-processing and a posteriori estimates, M. Křížek, P. Neittaanmäki, R. Stenberg (eds.), Marcel Dekker, New York, 1998, pp. 269–285. (1998) Zbl0902.65046MR1602738
  24. The derivative optimal point of the stresses for second order finite element method, Natur. Sci. J. Xiangtan Univ. 3 (1981), 36–45. (1981) 
  25. Natural inner superconvergence for the finite element method, In Proc. of the China-France Symposium on Finite Element Methods (Beijing 1982), Science Press, Gorden and Breach, Beijing, 1983, pp. 935–960. (1983) Zbl0611.65074MR0754041
  26. Uniform superconvergence estimates of derivatives for the finite element method, Numer. Math. J. Xiangtan Univ. 5. Zbl0549.65073MR0745576
  27. Uniform superconvergence estimates for the finite element method, Natur. Sci. J. Xiangtan Univ. (19851983), 10–26 311–318. (19851983) MR0890708
  28. The Superconvergence Theory of Finite Element Methods, Hunan Scientific and Technical Publishers, Changsha, 1989. (Chinese) (1989) 
  29. The superconvergence for the 3rd order triangular finite elements, (1997) (to appear). (ARRAY(0x8e7e6c0)) 
  30. Some superconvergence results in the finite element method, LN in Math. 606, (1977, 353–362), Springer, Berlin. (1977, 353–362) MR0488863

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.