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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 |
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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