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Study of the NIPG method for two–parameter singular perturbation problems on several layer adapted grids

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Abstract

In this paper, we apply the non-symmetric interior penalty Galerkin (NIPG) method to obtain the numerical solution of two-parameter singularly perturbed convection-diffusion-reaction boundary-value problems. In order to discretize the domain, here, we use the layer-adapted piecewise-uniform Shishkin mesh, the Bakhvalov mesh and the exponentially-graded mesh. We establish a superconvergence result of the NIPG method, that is, the proposed method is parameter-uniformly convergent with the order almost \((k+1)\) on the Shishkin mesh and \((k+1)\) on the Bakhvalov mesh and on the exponentially graded mesh in the energy norm, where k is the order of the polynomials. Numerical results comparing the three different types of meshes are presented at the end of the article supporting the theoretical error estimates.

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Acknowledgements

The authors wish to acknowledge the referees for providing valuable comments and suggestions.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Gautam Singh & Srinivasan Natesan

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  1. Gautam Singh
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  2. Srinivasan Natesan
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Correspondence to Srinivasan Natesan.

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Singh, G., Natesan, S. Study of the NIPG method for two–parameter singular perturbation problems on several layer adapted grids. J. Appl. Math. Comput. 63, 683–705 (2020). https://doi.org/10.1007/s12190-020-01334-7

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  • DOI: https://doi.org/10.1007/s12190-020-01334-7

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