Mathematics / Matematik

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

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Author: search.filters.author.Şendur, AliSubject: search.filters.subject.Finite element method

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Bubble-Based Stabilized Finite Element Methods for Time-Dependent Convection–diffusion–reaction Problems
    (John Wiley and Sons Inc., 2016) Şendur, Ali; Neslitürk, Ali İhsan
    In this paper, we propose a numerical algorithm for time-dependent convection–diffusion–reaction problems and compare its performance with the well-known numerical methods in the literature. Time discretization is performed by using fractional-step θ-scheme, while an economical form of the residual-free bubble method is used for the space discretization. We compare the proposed algorithm with the classical stabilized finite element methods over several benchmark problems for a wide range of problem configurations. The effect of the order in the sequence of discretization (in time and in space) to the quality of the approximation is also investigated. Numerical experiments show the improvement through the proposed algorithm over the classical methods in either cases.
  • 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.