On the convergence analysis of a time dependent elliptic equation with discontinuous coefficients

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.

Keywords

• elliptic equation
• discontinuous coefficient
• mortar spectral element method
• error analysis
• 35j57
• 65m70