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By Mr (review M (m, Jing (s-upps-it) Nordström and Reviewed M. K. Kadalbajoo


Interface procedures for finite difference approximations of the advection-diffusion equation. (English summary) J. Comput. Appl. Math. 236 (2011), no. 5, 602–620. The paper deals with interface procedures for solving the advection-diffusion equation. The main focus of the paper is, in addition to stability and accuracy properties of the schemes, to investigate the stiffness and the reflecting properties of the different interface treatment procedures. For the sake of clarity, a one-dimensional problem is considered in the paper. However, these formulations do extend to higher space dimensional problems and with more general boundary conditions. Wellposed conditions for the continuous advection-diffusion problems are derived and several discrete approximations are considered, which are analysed for stability by the energy method and also by spectral analysis. Several numerical experiments are carried out for comparison of different interface procedures (the Baumann-Oden method, the Carpenter-Nordstrom-Gotlieb method, and the local discontinuous Galerkin method) and the results presented. It is concluded that these interface procedures do not increase the spectral radius if the penalty parameters are suitably chosen

Year: 2013
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