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Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

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Abstract

We consider a singularly perturbed reaction-diffusion elliptic problem in two dimensions (x,y), with strongly anisotropic coefficients and line interface. The second order derivative with respect to x is multiplied by a small parameter ɛ2. We construct finite volume difference schemes on condensed Shihskin meshes and prove ɛ-uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.

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Authors and Affiliations

  1. University of Rousse, Studentska str. 8, 7017, Rousse, Bulgaria

    I. Braianov

  2. University of Rousse, Studentska str. 8, 7017, Rousse, Bulgaria

    L. Vulkov

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  1. I. Braianov
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  2. L. Vulkov
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Correspondence to I. Braianov.

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Braianov, I., Vulkov, L. Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy. Computing 71, 153–173 (2003). https://doi.org/10.1007/s00607-003-0009-3

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  • DOI: https://doi.org/10.1007/s00607-003-0009-3

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