Mathematics / Matematik

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

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Subject: search.filters.subject.Finite element methodWoS 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: 55
    Citation - Scopus: 56
    Two-Level Finite Element Method With a Stabilizing Subgrid for the Incompressible Mhd Equations
    (John Wiley and Sons Inc., 2010) Aydın, Selçuk Han; Neslitürk, Ali İhsan; Tezer Sezgin, Münevver
    We consider the Galerkin finite element method (FEM) for the incompressible magnetohydrodynamic (MHD) equations in two dimension. The domain is discretized into a set of regular triangular elements and the finite-dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual-free bubble functions. To find the bubble part of the solution, a two-level FEM with a stabilizing subgrid of a single node is described and its application to the MHD equations is displayed. Numerical approximations employing the proposed algorithm are presented for three benchmark problems including the MHD cavity flow and the MHD flow over a step. The results show that the proper choice of the subgrid node is crucial to get stable and accurate numerical approximations consistent with the physical configuration of the problem at a cheap computational cost. Furthermore, the approximate solutions obtained show the well-known characteristics of the MHD flow. Copyright © 2009 John Wiley & Sons, Ltd.