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A Two-Grid Method on Layer-Adapted Meshes for a Semilinear 2D Reaction-Diffusion Problem

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Large-Scale Scientific Computing (LSSC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5910))

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Abstract

A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discetizied by a two-grid scheme on layer-adapted meshes. In the first step, the nonlinear problem is discretized on coarse grid. In the second step, the problem is discretized on a fine grid and linearized around the interpolation of the computed solution on the first step. We show theoretically and numerically that the global error on Shishkin or Bakhvalov mesh is the same as would have been obtained if the nonlinear problem had been solved directly on the fine grid.

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References

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Authors and Affiliations

  1. Faculty of Natural Science and Education, University of Rousse, 8 Studentska str., Rousse, 7017, Bulgaria

    Ivanka T. Angelova & Lubin G. Vulkov

Authors
  1. Ivanka T. Angelova
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  2. Lubin G. Vulkov
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Editors and Affiliations

  1. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 25A, 1113, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25-A, 1113, Sofia, Bulgaria

    Svetozar Margenov

  3. Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads - Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Angelova, I.T., Vulkov, L.G. (2010). A Two-Grid Method on Layer-Adapted Meshes for a Semilinear 2D Reaction-Diffusion Problem. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2009. Lecture Notes in Computer Science, vol 5910. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12535-5_84

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  • DOI: https://doi.org/10.1007/978-3-642-12535-5_84

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12534-8

  • Online ISBN: 978-3-642-12535-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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