Abstract
Abstract In this paper, we consider a heat equation with diffusion coefficient that varies depending on the heterogeneity of the domain. We propose a spectral elements discretization of this problem with the mortar domain decomposition method on the space variable and Euler’s implicit scheme with respect to the time. The convergence analysis and an optimal error estimates are proved.
Highlights
This paper is devoted to the numerical analysis of the mortar spectral element discretization of the heat equation in an heterogenous medium with a variable di usion coe cient λ formulated by the problem (1)
The a priori and a posteriori analysis were proposed based on the nite element method and the spectral discretization
We prove that the discrete problem is well posed and we show an optimal error estimate for a good choice of domain decomposition
Summary
We propose a spectral elements discretization of this problem with the mortar domain decomposition method on the space variable and Euler’s implicit scheme with respect to the time. We prove that the discrete problem is well posed and we show an optimal error estimate for a good choice of domain decomposition. We suppose that the restriction of the function λ on each sub-domain Ω◦i , ≤ i ≤ I◦ is constant.
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