Mathematics / Matematik

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

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End date: 2009Subject: search.filters.subject.Finite element method

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 11
    Citation - Scopus: 10
    A Stabilizing Subgrid for Convection-Diffusion Problem
    (World Scientific Publishing Co. Pte Ltd, 2006) Neslitürk, Ali İhsan
    A stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection-diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 40
    Finite Element Method Solution of Electrically Driven Magnetohydrodynamic Flow
    (Elsevier Ltd., 2006) Neslitürk, Ali İhsan; Tezer, Münevver
    The magnetohydrodynamic (MHD) flow in a rectangular duct is investigated for the case when the flow is driven by the current produced by electrodes, placed one in each of the walls of the duct where the applied magnetic field is perpendicular. The flow is steady, laminar and the fluid is incompressible, viscous and electrically conducting. A stabilized finite element with the residual-free bubble (RFB) functions is used for solving the governing equations. The finite element method employing the RFB functions is capable of resolving high gradients near the layer regions without refining the mesh. Thus, it is possible to obtain solutions consistent with the physical configuration of the problem even for high values of the Hartmann number. Before employing the bubble functions in the global problem, we have to find them inside each element by means of a local problem. This is achieved by approximating the bubble functions by a nonstandard finite element method based on the local problem. Equivelocity and current lines are drawn to show the well-known behaviours of the MHD flow. Those are the boundary layer formation close to the insulated walls for increasing values of the Hartmann number and the layers emanating from the endpoints of the electrodes. The changes in direction and intensity with respect to the values of wall inductance are also depicted in terms of level curves for both the velocity and the induced magnetic field.
  • 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.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 16
    The Nearly-Optimal Petrov-Galerkin Method for Convection-Diffusion Problems
    (Elsevier Ltd., 2003) Neslitürk, Ali İhsan; Harari, Isaac
    The nearly-optimal Petrov-Galerkin (NOPG) method is employed to improve finite element computation of convection-dominated transport phenomena. The design of the NOPG method for convection-diffusion is based on consideration of the advective limit. Nonetheless, the resulting method is applicable to the entire admissible range of problem parameters. An investigation of the stability properties of this method leads to a coercivity inequality. The convergence features of the NOPG method for convection-diffusion are studied in an error analysis that is based on the stability estimates. The proposed method compares favorably to the performance of an established technique on several numerical tests.