| Title:
|
Some $L_2$-error estimates for semi-variational method applied to parabolic equations (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
5 |
| Year:
|
1974 |
| Pages:
|
327-341 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The convergence of the semi-variational approximations to the solution of a mixed parabolic problem is investigated. The derivation of an estimate in $L_2$-norm follows the approach suggested by Dupont, using a parabolic regularity and a projection introduced by Bramble and Osborn. As a result, the second semi-variational approximation is found to possess the maximal possible order of accuracy in space and the fourth order in time. () |
| MSC:
|
35K30 |
| MSC:
|
65M99 |
| MSC:
|
65N30 |
| MSC:
|
65N99 |
| idZBL:
|
Zbl 0316.65022 |
| idMR:
|
MR0378447 |
| DOI:
|
10.21136/AM.1974.103549 |
| . |
| Date available:
|
2008-05-20T17:59:45Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103549 |
| . |
| Reference:
|
[1] I. Hlaváček: On a semi-variational method for parabolic equations.Aplikace matematiky 17 (1972), 5, 327-351, 18 (1973), l, 43-64. |
| Reference:
|
[2] J. Douglas, Jr. T. Dupont: Galerkin methods for parabolic equations.SIAM J. Numer. Anal. 7(1970), 4, 575-626. |
| Reference:
|
[3] T. Dupont: Some $L^2$ error estimates for parabolic Galerkin methods. |
| Reference:
|
[4] J. H. Bramble J. E. Osborn: Rate of convergence estimates for non-self adjoint eigenvalue approximations.MRC Report 1232, Univ. Wisconsin, 1972. |
| Reference:
|
[5] J. L. Lions: Equations differentielles operationelles et problèmes aux limites.Springer-Verlag, Berlin, 1961. MR 0153974 |
| . |
