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.
Keywords: heat equation; diffusion coefficient; spectral element methods; a priori estimates
DOI: DOI 10.14712/1213-7243.2015.160
AMS Subject Classification: 35K05 65N35 35B45