Mathematics / Matematik

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

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Author: search.filters.author.Kaya, AdemSubject: search.filters.subject.Finite element method

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 29
    Citation - Scopus: 35
    Finite Difference Approximations of Multidimensional Unsteady Convection-Diffusion Equations
    (Elsevier Ltd., 2015) Kaya, Adem
    In this paper, the numerical approximation of unsteady convection-diffusion-reaction equations with finite difference method on a special grid is studied in the convection or reaction-dominated regime. We extend the method [19] which was designed for multidimensional steady convection-diffusion-reaction equations to unsteady problems. We investigate two possible different ways of combining the discretization in time and in space (where the sequence of the discretizations is interchanged). Discretization in time is performed by using Crank-Nicolson and Backward-Euler finite difference schemes, while for the space discretization we consider the method [19]. Numerical tests are presented to show good performance of the method.
  • 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: 15
    Citation - Scopus: 18
    A Finite Difference Scheme for Multidimensional Convection-Diffusion Equations
    (Elsevier, 2014) Kaya, Adem
    In this paper a finite difference scheme is proposed for multidimensional convection-diffusion-reaction equations, particularly designed to treat the most interesting case of small diffusion. It is based closely on the work S¸endur and Neslitu¨rk (2011). Application of the method to multidimensional convection-diffusion-reaction equation is based on a simple splitting of the convection-diffusion-reaction equation and then joining their approximations obtained with S¸endur and Neslitu¨rk (2011). The method adapts very well to all regimes with continuous transitions from one regime to another. Numerical tests show good performance of the method and superiority with respect to well known stabilized finite element methods.