Mathematics / Matematik

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

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Publication Index: search.filters.publicationIndex.ScopusSubject: search.filters.subject.Convection-diffusion

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  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Finite Difference Approximations of Multidimensional Convection-Diffusion Problems With Small Diffusion on a Special Grid
    (Elsevier Ltd., 2015) Kaya, Adem; Şendur, Ali
    A numerical scheme for the convection-diffusion-reaction (CDR) problems is studied herein. We propose a finite difference method on a special grid for solving CDR problems particularly designed to treat the most interesting case of small diffusion. We use the subgrid nodes in the Link-cutting bubble (LCB) strategy [5] to construct a numerical algorithm that can easily be extended to the higher dimensions. The method adapts very well to all regimes with continuous transitions from one regime to another. We also compare the performance of the present method with the Streamline-upwind Petrov-Galerkin (SUPG) and the Residual-Free Bubbles (RFB) methods on several benchmark problems. The numerical experiments confirm the good performance of the proposed method.
  • 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.