Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5830
Title: Finite difference approximations of multidimensional convection-diffusion-reaction problems with small diffusion on a special grid
Authors: Kaya, Adem
Şendur, Ali
Keywords: Finite element method
Finite difference method
Non-uniform grid
Singular perturbation
Convection-diffusion
Issue Date: Nov-2015
Publisher: Elsevier Ltd.
Source: Kaya, A., and Şendur, A. (2015). Finite difference approximations of multidimensional convection-diffusion-reaction problems with small diffusion on a special grid. Journal of Computational Physics, 300, 574-591. doi:10.1016/j.jcp.2015.08.007
Abstract: A numerical scheme for the convection-diffusion-reaction (CDR) problems is studied herein. We propose a finite difference method on a special grid for solving CDR problems particularly designed to treat the most interesting case of small diffusion. We use the subgrid nodes in the Link-cutting bubble (LCB) strategy [5] to construct a numerical algorithm that can easily be extended to the higher dimensions. The method adapts very well to all regimes with continuous transitions from one regime to another. We also compare the performance of the present method with the Streamline-upwind Petrov-Galerkin (SUPG) and the Residual-Free Bubbles (RFB) methods on several benchmark problems. The numerical experiments confirm the good performance of the proposed method.
URI: https://doi.org/10.1016/j.jcp.2015.08.007
http://hdl.handle.net/11147/5830
ISSN: 0021-9991
0021-9991
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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