Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Şendur, AliPublisher: search.filters.publisher.Elsevier Ltd.

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  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Finite Difference Approximations of Multidimensional Convection-Diffusion Problems With Small Diffusion on a Special Grid
    (Elsevier Ltd., 2015) Kaya, Adem; Şendur, Ali
    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.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Applications of the Pseudo Residual-Free Bubbles To the Stabilization of the Convection-Diffusion Problems in 2d
    (Elsevier Ltd., 2014) Şendur, Ali; Neslitürk, Ali İhsan; Kaya, Adem
    A stabilized finite element method is studied herein for two-dimensional convection-diffusion-reaction problems. The method is based on the residual-free bubbles (RFB) method. However we replace the RFB functions by their cheap, yet efficient approximations computed on a specially chosen subgrid, which retain the same qualitative behavior. Since the correct spot of subgrid points plays a crucial role in the approximation, it is important to determine their optimal locations, which we do it through a minimization process with respect to the L1-norm. The resulting numerical method has similar stability features with the well-known stabilized methods in the literature for the whole range of problem parameters and this fact is also confirmed by numerical experiments.