Thirty years from the discovery of superconvergence of the finite elements method

Jan Brandts; Michal Křížek

Pokroky matematiky, fyziky a astronomie (2003)

  • Volume: 48, Issue: 4, page 288-293
  • ISSN: 0032-2423

How to cite

top

Brandts, Jan, and Křížek, Michal. "Třicet let od objevu superkonvergence metody konečných prvků." Pokroky matematiky, fyziky a astronomie 48.4 (2003): 288-293. <http://eudml.org/doc/196757>.

@article{Brandts2003,
author = {Brandts, Jan, Křížek, Michal},
journal = {Pokroky matematiky, fyziky a astronomie},
language = {cze},
number = {4},
pages = {288-293},
publisher = {Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists},
title = {Třicet let od objevu superkonvergence metody konečných prvků},
url = {http://eudml.org/doc/196757},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Brandts, Jan
AU - Křížek, Michal
TI - Třicet let od objevu superkonvergence metody konečných prvků
JO - Pokroky matematiky, fyziky a astronomie
PY - 2003
PB - Jednota českých matematiků a fyziků Union of Czech Mathematicians and Physicists
VL - 48
IS - 4
SP - 288
EP - 293
LA - cze
UR - http://eudml.org/doc/196757
ER -

References

top
  1. Babuška, I., Práger, M., Vitásek, E., Numerical processes in differential equations, John Wiley & Sons, New York 1966. (1966) Zbl0156.16003MR0223101
  2. Bakker, M., A note on C 0 Galerkin methods for two-point boundary problem, Numer. Math. 38 (1981/82), 447–453. (1981) MR0654109
  3. Blum, H., Lin, Q., Rannacher, R., Asymptotic error expansion and Richardson extrapolation for linear finite elements, Numer. Math. 49 (1986), 11–38. (1986) Zbl0594.65082MR0847015
  4. Brandts, J., Křížek, M., History and future of superconvergence in three-dimensional finite element methods, Proc. Conf. Finite Element Methods: Three-dimensional Problems, GAKUTO Internat. Ser. Math. Sci. Appl., vol. 15, Gakkōtosho, Tokyo 2001, 22–33. (2001) Zbl0994.65114MR1896264
  5. Douglas, J., Dupont, T., Some superconvergence results for Galerkin methods for the approximate solution of two-point boundary value problems, Topics in Numer. Anal. II, Acad. Press 1973, 89–113. (1973) Zbl0277.65052MR0366044
  6. Chen, C. M., Huang, Y. Q., High accuracy theory of finite element methods, Hunan Science and Technology Press, Changsha 1995. (1995) 
  7. Hlaváček, I., Chleboun, J., A recovered gradient method applied to smooth optimal shape problems, Appl. Math. 41 (1996), 281–297. (1996) Zbl0870.65050MR1395687
  8. Křížek, M., Padesát let metody konečných prvků, PMFA 37 (1992), 129–140. (1992) 
  9. Křížek, M., Neittaanmäki, P., On superconvergence techniques, Acta Appl. Math. 9 (1987), 175–198. (1987) Zbl0624.65107MR0900263
  10. Křížek, M., Neittaanmäki, P., Stenberg, R., Finite Element Methods: Superconvergence, Postprocessing, and A Posteriori Estimates, LN in Pure and Appl. Math., vol. 196, Marcel Dekker, New York 1998. (1998) Zbl0884.00048MR1602809
  11. Lesaint, P., Zlámal, M., Superconvergence of the gradient of finite element solutions, RAIRO Anal. Numér. 13 (1979), 139–166. (1979) Zbl0412.65051MR0533879
  12. Oganesjan, L. A., Ruchovec, L. A., An investigation of the rate of convergence of variational-difference schemes for second order elliptic equations in a two-dimensional region with smooth boundary, Ž. Vyčisl. Mat. i Mat. Fiz. 9 (1969), 1102–1120. (1969) MR0295599
  13. Taylor, A. E., Úvod do funkcionální analýzy, Academia, Praha 1973. (1973) 
  14. Wahlbin, L., Superconvergence in Galerkin finite element methods, LN in Math., vol. 1605, Springer, Berlin 1995. (1605) Zbl0826.65092MR1439050
  15. Zlámal, M., On the finite element method, Numer. Math. 12 (1968), 394–409. (1968) Zbl0176.16001
  16. Zlámal, M., Superconvergence and reduced integration in the finite element method, Math. Comp. 32 (1978), 663–685. (1978) Zbl0448.65068MR0495027

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.