Geodesic
Spectral element discretization of the heat equation with variable diffusion coefficient
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 2, pp. 185-200.

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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.
DOI : 10.14712/1213-7243.2015.160
Classification : 35B45, 35K05, 65N35
Keywords: heat equation; diffusion coefficient; spectral element methods; a priori estimates 
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Daikh, Y.; Chikouche, W. Spectral element discretization of the heat equation with variable diffusion coefficient. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 2, pp. 185-200. doi : 10.14712/1213-7243.2015.160. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.160/

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