On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation

Song Wang, L. Angermann

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    2 Citations (Scopus)

    Abstract

    This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.
    Original languageEnglish
    Pages (from-to)493-512
    JournalComputational Methods in Applied Mathematics
    Volume3
    Issue number3
    Publication statusPublished - 2003

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    Anisotropic Mesh
    Mesh Refinement
    Convection-diffusion Equation
    Finite volume method
    Singularly Perturbed
    Finite Volume Method
    Norm
    Petrov-Galerkin Method
    Galerkin Finite Element Method
    Bilinear form
    Approximation Error
    Energy
    Convergence Analysis
    Diffusion Coefficient
    Boundary Layer
    Two Dimensions
    Boundary layers
    Rate of Convergence
    Exact Solution
    Mesh

    Cite this

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    title = "On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation",
    abstract = "This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.",
    author = "Song Wang and L. Angermann",
    year = "2003",
    language = "English",
    volume = "3",
    pages = "493--512",
    journal = "Computational Methods in Applied Mathematics",
    issn = "1609-4840",
    publisher = "Walter de Gruyter GmbH (European Journal of Nanomedicine)",
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    TY - JOUR

    T1 - On Convergence of the Exponentially Fitted Finite Volume Method with an Anisotropic Mesh Refinement for a Singularly Perturbed Convection-Diffusion Equation

    AU - Wang, Song

    AU - Angermann, L.

    PY - 2003

    Y1 - 2003

    N2 - This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.

    AB - This paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. It is also shown that the approximation error in the discrete energy norm is bounded above by C(h ½ +h√|lnε/lnh|) with C independent of the mesh parameter h,, the diffusion coefficient ε, and the exact solution of the problem. Numerical results are presented to verify the theoretical rates of convergence.

    M3 - Article

    VL - 3

    SP - 493

    EP - 512

    JO - Computational Methods in Applied Mathematics

    JF - Computational Methods in Applied Mathematics

    SN - 1609-4840

    IS - 3

    ER -