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Uniformly Convergent High-Order Schemes for a 2D Elliptic Reaction-Diffusion Problem with Anisotropic Coefficients

  • Iliya Brayanov
  • Ivanka Dimitrova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2542)

Abstract

Two dimensional elliptic reaction - diffusion problem with highly anisotropic coefficients is considered. The second order derivative with respect to one of the independent variables is multiplied by a small parameter ∈. In this work, we construct and study finite difference schemes, defined on a priori Shishkin meshes, uniformly convergent with respect to the small parameter ∈, which have order three except for a logarithmic factor. Numerical experiments confirming the theoretical results are given.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Iliya Brayanov
    • 1
  • Ivanka Dimitrova
    • 1
  1. 1.Department of MathematicsUniversity of RousseRousseBulgaria

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