Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

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Author: search.filters.author.Şendur, AliWoS Q: search.filters.wosQuartile.Q2

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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: 1
    Citation - Scopus: 1
    A Fully Discrete ?-Uniform Method for Singular Perturbation Problems on Equidistant Meshes
    (Taylor and Francis Ltd., 2012) Filiz, Ali; Neslitürk, Ali; Şendur, Ali
    We propose a fully discrete ε-uniform finite-difference method on an equidistant mesh for a singularly perturbed two-point boundary-value problem (BVP). We start with a fitted operator method reflecting the singular perturbation nature of the problem through a local BVP. However, to solve the local BVP, we employ an upwind method on a Shishkin mesh in local domain, instead of solving it exactly. Thus, we show that it is possible to develop a ε-uniform method, totally in the context of finite differences, without solving any differential equation exactly. We further study the convergence properties of the numerical method proposed and prove that it nodally converges to the true solution for any ε. Finally, a set of numerical experiments is carried out to validate the theoretical results computationally. © 2012 Copyright Taylor and Francis Group, LLC