Spectral element discretization of the heat equation with variable diffusion coefficient
Commentationes Mathematicae Universitatis Carolinae (2016)
- Volume: 57, Issue: 2, page 185-200
- ISSN: 0010-2628
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topDaikh, Y., and Chikouche, W.. "Spectral element discretization of the heat equation with variable diffusion coefficient." Commentationes Mathematicae Universitatis Carolinae 57.2 (2016): 185-200. <http://eudml.org/doc/280134>.
@article{Daikh2016,
abstract = {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.},
author = {Daikh, Y., Chikouche, W.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {heat equation; diffusion coefficient; spectral element methods; a priori estimates},
language = {eng},
number = {2},
pages = {185-200},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Spectral element discretization of the heat equation with variable diffusion coefficient},
url = {http://eudml.org/doc/280134},
volume = {57},
year = {2016},
}
TY - JOUR
AU - Daikh, Y.
AU - Chikouche, W.
TI - Spectral element discretization of the heat equation with variable diffusion coefficient
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 2
SP - 185
EP - 200
AB - 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.
LA - eng
KW - heat equation; diffusion coefficient; spectral element methods; a priori estimates
UR - http://eudml.org/doc/280134
ER -
References
top- Bergam A., Bernardi C., Mghazli Z., 10.1090/S0025-5718-04-01697-7, Math. Comp. 74 (2005), 1117–1138. Zbl1072.65124MR2136996DOI10.1090/S0025-5718-04-01697-7
- Bernardi C., Maday Y., Spectral Methods, Handbook of Numerical Analysis V, P.G. Ciarlet and J.-L. Lions, Eds., North-Holland, Amsterdam, 1997. Zbl0929.35001MR1470226
- Bernardi C., Maday Y., Rapetti F., Discrétisations variationnelles de problèmes aux limites elliptiques, Mathématiques et Applications, 45, Springer, Berlin, 2004. Zbl1063.65119MR2068204
- 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. MR3215895
- Lions J.-L., Magenes E., Problèmes aux limites non homogènes et applications, vol. 1, Dunod, Paris, 1968. Zbl0212.43801MR0247243
- Thomée V., Galerkin Finite Element Methods for Parabolic Problems, Springer Series in Computational Mathematics, 25, Springer, Berlin, 1997. MR1479170
- Touihri M., Discrétisation spectrale des equations de Navier-Stokes à densité variable, PhD, Pierre et Marie Curie University, Paris 6, France, 1997.
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