WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7150

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2005 - 200912010 - 20132

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Subject: search.filters.subject.Stabilized FEM

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  • Article
    Citation - Scopus: 1
    Pseudo-Multi Functions for the Stabilization of Convection-Diffusion Equations on Rectangular Grids
    (Begell House Inc., 2013) Neslitürk, Ali İhsan; Baysal, Onur
    We propose a finite element method of Petrov-Galerkin type for a singularly perturbed convection diffusion problem on a discretization consisting of rectangular elements. The method is based on enriching the finite-element space with a combination of multiscale and residual-free bubble functions. These functions require the solution of the original differential problem, which makes the method quite expensive, especially in two dimensions. Therefore, we instead employ their cheap, yet efficient approximations, using only a few nodes in each element. Several numerical tests confirm the good performance of the corresponding numerical method.
  • 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
    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.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 67
    The Finite Element Method for Mhd Flow at High Hartmann Numbers
    (Elsevier Ltd., 2005) Neslitürk, Ali İhsan; Tezer, Münevver
    A stabilized finite element method using the residual-free bubble functions (RFB) is proposed for solving the governing equations of steady magnetohydrodynamic duct flow. A distinguished feature of the RFB method is the resolving capability of high gradients near the layer regions without refining mesh. We show that the RFB method is stable by proving that the numerical method is coercive even not only at low values but also at moderate and high values of the Hartmann number. Numerical results confirming theoretical findings are presented for several configurations of interest. The approximate solution obtained by the RFB method is also compared with the analytical solution of Shercliff's problem.