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.Neslitürk, Ali İhsanSubject: search.filters.subject.Diffusion in liquids

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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; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    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: 10
    On the Choice of Stabilizing Sub-Grid for Convection-Diffusion Problem on Rectangular Grids
    (Elsevier Ltd., 2010) Neslitürk, Ali İhsan; Neslitürk, Ali İhsan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    A stabilizing sub-grid which consists of a single additional node in each rectangular element is analyzed for solving the convection-diffusion problem, especially in the case of small diffusion. We provide a simple recipe for spotting the location of the additional node that contributes a very good stabilizing effect to the overall numerical method. We further study convergence properties of the method under consideration and prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfies the same type of a priori error estimates that are typically obtained with the SUPG method. Some numerical experiments that confirm the theoretical findings are also presented. © 2010 Elsevier Ltd. All rights reserved.