73 research outputs found

    The finite volume method based on stabilized finite element for the stationary Navier–Stokes problem

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    AbstractA finite volume method based on stabilized finite element for the two-dimensional stationary Navier–Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. We obtain the well-posedness of the FVM based on stabilized finite element for the stationary Navier–Stokes equations. Moreover, for quadrilateral and triangular partition, the optimal H1 error estimate of the finite volume solution uh and L2 error estimate for ph are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM

    A Subgrid Model for the Time-Dependent Navier-Stokes Equations

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    Numerical analysis of an implicit fully discrete local discontinuous Galerkin method for the fractional Zakharov–Kuznetsov equation

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    In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L 2 error estimate for the linear case with the convergence rate  through analysis

    Stability and convergence for the reform postprocessing Galerkin method, Nonlinear Anal

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    Citation for published version (APA): . Stability and convergence for the reform postprocessing Galerkin method. (RANA : reports on applied and numerical analysis; Vol. 9823). Eindhoven: Technische Universiteit Eindhoven. Document status and date: Published: 01/01/1998 Document Version: Publisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected] providing details and we will investigate your claim. In this article we investigate the discretization in time of numerical schemes based on the reform postprocessing Galerkin method for the two-dimensional Navier-Stokes equations. The approximate solution is computed as the sum of a low frequence component given by treating the nonlinearity in a small space and a high frequence one given by treating the linearity in a large space. Moreover, we give the stability and convergence analysis of the numerical solutions corresponding to the standard Galerkin method and the reform postprocessing Galerkin method. Our results show that the reform postprocessing Galerkin method is of the same stability and convergence rate as the standard Galerkin method with high modes which needs treating the nonlinearity in a large space. Hence, our method should yield a significant gain in computing time
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