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

    Research output: Contribution to journalArticle

    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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