| Title:
|
On a semi-variational method for parabolic equations. I (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
17 |
| Issue:
|
5 |
| Year:
|
1972 |
| Pages:
|
327-351 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper aims at a further development of the finite element method, when applied to mixed problems for parabolic equations. Much work has been done on a special Galerkin-type procedure of order $\tau^2$, which is similar to the Crank-Nicholson finite-difference scheme. Here a sequence of approximations is presented, possessing an increasing accuracy in the time increment $\tau$. The first approximation coincides with the above-mentioned procedure. For the second approximation, the rate of convergence $\tau^4$ and the stability with respect to the initial condition is proved. The efficiency of the first and second approximations are compared on a numerical example. () |
| MSC:
|
35K99 |
| MSC:
|
65M15 |
| MSC:
|
65M99 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0246.65030 |
| idMR:
|
MR0314285 |
| DOI:
|
10.21136/AM.1972.103427 |
| . |
| Date available:
|
2008-05-20T17:54:18Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103427 |
| . |
| Reference:
|
[1] J. Douglas, Jr. T. Dupont: Galerkin methods for parabolic equations.SIAM J. Numer. Anal. 7(1970), 4, 575-626. MR 0277126 |
| Reference:
|
[2] I. Hlaváček: Variational formulation of the Cauchy problem for equations with operator coefficients.Aplikace matematiky 16 (1971), 1, 46-63. MR 0283652 |
| Reference:
|
[3] I. Hlaváček: Variational principles for parabolic equations.Aplikace matematiky 14 (1969), 4, 278-297. MR 0255988 |
| Reference:
|
[4] E. L. Wilson R. E. Nickell: Application of the finite element method to heat conduction analysis.Nucl. Eng. and Design 4 (1966), 276-286. 10.1016/0029-5493(66)90051-3 |
| Reference:
|
[5] J. L. Lions: Equations differentielles operationelles et problèmes aux limites.Grundlehren Math. Wiss. Bd. 111, Springer 1961. MR 0153974 |
| Reference:
|
[6] G. Birkhoff M. H. Schultz R. S. Varga: Piecewise Hermite interpolation in one and two variables with application to partial differential equations.Numerische Math. 11 (1968), 232-256. MR 0226817, 10.1007/BF02161845 |
| Reference:
|
[7] А. А. Самарский: Некоторые вопросы общей теории разностных схем.Сб. ,,Дифференциалные уравнения с частными производными." Издат. Наука, Москва 1970. |
| Reference:
|
[8] A. Ralston: A first course in numerical analysis.Mc Graw-Hill, 1965. Zbl 0139.31603, MR 0191070 |
| . |
