A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation

Song Wang, Z-C. Li

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ɛ. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular elements. It is shown that the method is stable with respect to a semi-discrete energy norm and the approximation error in the semi-discrete energy norm is bounded by Ch√|1nɛ/1nh| with C independent of the mesh parameter h, the diffusion coefficient ɛ and the exact solution of the problem.
    Original languageEnglish
    Pages (from-to)1689-1709
    JournalMathematics of Computation
    Volume72
    Issue number244
    DOIs
    Publication statusPublished - 2003

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    Anisotropic Mesh
    Mesh Refinement
    Convection-diffusion Equation
    Finite volume method
    Singularly Perturbed
    Finite Volume Method
    Triangular
    Finite Element Method
    Norm
    Finite element method
    Singularly Perturbed Problem
    Convection-diffusion Problems
    Discretization Method
    Approximation Error
    Singular Perturbation
    Energy
    Piecewise Linear
    Galerkin
    Diffusion Coefficient
    Exact Solution

    Cite this

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    title = "A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation",
    abstract = "In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ɛ. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular elements. It is shown that the method is stable with respect to a semi-discrete energy norm and the approximation error in the semi-discrete energy norm is bounded by Ch√|1nɛ/1nh| with C independent of the mesh parameter h, the diffusion coefficient ɛ and the exact solution of the problem.",
    author = "Song Wang and Z-C. Li",
    year = "2003",
    doi = "10.1090/S0025-5718-03-01516-3",
    language = "English",
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    journal = "Mathematics of Computation",
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    publisher = "American Mathematical Society",
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    TY - JOUR

    T1 - A nonconforming combination of the finite element and volume methods with an anisotropic mesh refinement for a singularly perturbed convection-diffusion equation

    AU - Wang, Song

    AU - Li, Z-C.

    PY - 2003

    Y1 - 2003

    N2 - In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ɛ. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular elements. It is shown that the method is stable with respect to a semi-discrete energy norm and the approximation error in the semi-discrete energy norm is bounded by Ch√|1nɛ/1nh| with C independent of the mesh parameter h, the diffusion coefficient ɛ and the exact solution of the problem.

    AB - In this paper we formulate and analyze a discretization method for a 2D linear singularly perturbed convection-diffusion problem with a singular perturbation parameter ɛ. The method is based on a nonconforming combination of the conventional Galerkin piecewise linear triangular finite element method and an exponentially fitted finite volume method, and on a mixture of triangular and rectangular elements. It is shown that the method is stable with respect to a semi-discrete energy norm and the approximation error in the semi-discrete energy norm is bounded by Ch√|1nɛ/1nh| with C independent of the mesh parameter h, the diffusion coefficient ɛ and the exact solution of the problem.

    U2 - 10.1090/S0025-5718-03-01516-3

    DO - 10.1090/S0025-5718-03-01516-3

    M3 - Article

    VL - 72

    SP - 1689

    EP - 1709

    JO - Mathematics of Computation

    JF - Mathematics of Computation

    SN - 0025-5718

    IS - 244

    ER -