| Title:
|
Třicet let od objevu superkonvergence metody konečných prvků (Czech) |
| Title:
|
Thirty years from the discovery of superconvergence of the finite elements method (English) |
| Author:
|
Brandts, Jan |
| Author:
|
Křížek, Michal |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
288-293 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65-xx |
| . |
| Date available:
|
2010-12-11T20:07:54Z |
| Last updated:
|
2012-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141190 |
| . |
| Reference:
|
[1] Babuška, I., Práger, M., Vitásek, E.: Numerical processes in differential equations.John Wiley & Sons, New York 1966. MR 0223101 |
| Reference:
|
[2] Bakker, M.: A note on $C^0$ Galerkin methods for two-point boundary problem.Numer. Math. 38 (1981/82), 447–453. MR 0654109 |
| Reference:
|
[3] Blum, H., Lin, Q., Rannacher, R.: Asymptotic error expansion and Richardson extrapolation for linear finite elements.Numer. Math. 49 (1986), 11–38. Zbl 0594.65082, MR 0847015 |
| Reference:
|
[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. MR 1896264 |
| Reference:
|
[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. MR 0366044 |
| Reference:
|
[6] Chen, C. M., Huang, Y. Q.: High accuracy theory of finite element methods.Hunan Science and Technology Press, Changsha 1995. |
| Reference:
|
[7] Hlaváček, I., Chleboun, J.: A recovered gradient method applied to smooth optimal shape problems.Appl. Math. 41 (1996), 281–297. MR 1395687 |
| Reference:
|
[8] Křížek, M.: Padesát let metody konečných prvků.PMFA 37 (1992), 129–140. |
| Reference:
|
[9] Křížek, M., Neittaanmäki, P.: On superconvergence techniques.Acta Appl. Math. 9 (1987), 175–198. MR 0900263 |
| Reference:
|
[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. MR 1602809 |
| Reference:
|
[11] Lesaint, P., Zlámal, M.: Superconvergence of the gradient of finite element solutions.RAIRO Anal. Numér. 13 (1979), 139–166. MR 0533879 |
| Reference:
|
[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. MR 0295599 |
| Reference:
|
[13] Taylor, A. E.: Úvod do funkcionální analýzy.Academia, Praha 1973. |
| Reference:
|
[14] Wahlbin, L.: Superconvergence in Galerkin finite element methods.LN in Math., vol. 1605, Springer, Berlin 1995. MR 1439050 |
| Reference:
|
[15] Zlámal, M.: On the finite element method.Numer. Math. 12 (1968), 394–409. |
| Reference:
|
[16] Zlámal, M.: Superconvergence and reduced integration in the finite element method.Math. Comp. 32 (1978), 663–685. MR 0495027 |
| . |
