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Superconvergence of discontinuous Galerkin method with interior penalties for singularly perturbed two-point boundary-value problems

  • Gautam Singh
  • Srinivasan Natesan
Article
  • 39 Downloads

Abstract

In this paper, superconvergence properties of the discontinuous Galerkin method for singularly perturbed two-point boundary-value problems of reaction–diffusion and convection–diffusion types are studied. By using piecewise polynomials of degree k on modified Shishkin mesh, superconvergence error bounds of \((N^{-1}\ln N)^{k+1}\) in the discrete energy norm are established, where N is the number of elements. Finally, the convergence result is verified numerically.

Keywords

Singularly perturbed differential equation Discontinuous Galerkin finite element method Shishkin mesh Superconvergence 

Mathematics Subject Classification

65L11 65L20 65L60 65L70 

Notes

Acknowledgements

The authors express their sincere gratitude to the referee for his/her valuable comments and suggestions, which helped to improve the presentation.

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Copyright information

© Istituto di Informatica e Telematica (IIT) 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology GuwahatiGuwahatiIndia

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