| Title:
|
Spectral element discretization of the heat equation with variable diffusion coefficient (English) |
| Author:
|
Daikh, Y. |
| Author:
|
Chikouche, W. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
57 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
185-200 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We are interested in the discretization of the heat equation with a diffusion coefficient depending on the space and time variables. The discretization relies on a spectral element method with respect to the space variables and Euler's implicit scheme with respect to the time variable. A detailed numerical analysis leads to optimal a priori error estimates. (English) |
| Keyword:
|
heat equation |
| Keyword:
|
diffusion coefficient |
| Keyword:
|
spectral element methods |
| Keyword:
|
a priori estimates |
| MSC:
|
35B45 |
| MSC:
|
35K05 |
| MSC:
|
65N35 |
| idZBL:
|
Zbl 1363.35146 |
| idMR:
|
MR3513444 |
| DOI:
|
10.14712/1213-7243.2015.160 |
| . |
| Date available:
|
2016-07-05T15:06:11Z |
| Last updated:
|
2018-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145756 |
| . |
| Reference:
|
[1] Bergam A., Bernardi C., Mghazli Z.: A posteriori analysis of the finite element discretization of some parabolic equations.Math. Comp. 74 (2005), 1117–1138. Zbl 1072.65124, MR 2136996, 10.1090/S0025-5718-04-01697-7 |
| Reference:
|
[2] Bernardi C., Maday Y.: Spectral Methods.Handbook of Numerical Analysis V, P.G. Ciarlet and J.-L. Lions, Eds., North-Holland, Amsterdam, 1997. Zbl 0929.35001, MR 1470226 |
| Reference:
|
[3] Bernardi C., Maday Y., Rapetti F.: Discrétisations variationnelles de problèmes aux limites elliptiques.Mathématiques et Applications, 45, Springer, Berlin, 2004. Zbl 1063.65119, MR 2068204 |
| Reference:
|
[4] Chorfi N., Abdelwahed M., Ben Omrane I.: A posteriori analysis of the spectral element discretization of the heat equation.An. Stiint. Univ. “Ovidius” Constanta Ser. Mat. 22 (2014), no. 3, 13–35. MR 3215895 |
| Reference:
|
[5] Lions J.-L., Magenes E.: Problèmes aux limites non homogènes et applications.vol. 1, Dunod, Paris, 1968. Zbl 0212.43801, MR 0247243 |
| Reference:
|
[6] Thomée V.: Galerkin Finite Element Methods for Parabolic Problems.Springer Series in Computational Mathematics, 25, Springer, Berlin, 1997. MR 1479170 |
| Reference:
|
[7] Touihri M.: Discrétisation spectrale des equations de Navier-Stokes à densité variable.PhD, Pierre et Marie Curie University, Paris 6, France, 1997. |
| . |
