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Non-Symmetric Interior Penalty Galerkin Finite Element Method for a Class of Singularly Perturbed Reaction Diffusion Problems with Discontinuous Data

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Abstract

This paper presents a non-symmetric interior penalty Galerkin finite element method for a class of one dimensional singularly perturbed reaction–diffusion problems with discontinuous coefficients. The solution of this class of problem has been observed to exhibit boundary and interior layers. The error estimates in the energy as well as the balanced norm have been derived. It has been observed that errors are uniform with respect to the perturbation parameter \(\varepsilon \). The numerical solution of the problem has been computed using the method proposed in the study to support the corresponding theoretical results. The uniformness of the error estimates with respect to the perturbation parameter \(\varepsilon \) has been established numerically for the \(L_\infty \)-norm.

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Funding

The research of the first author is supported by Council for Scientific and Industrial Research, New Delhi, India vide letter no. 09/045(1547)/2017-EMR-I. The research of the corresponding and third author is supported by Science and Engineering Research board, Department of Science and Technology, India via Grant No SPG/2022/000063.

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Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Ram Prasad Yadav & Pratima Rai

  2. Department of Mathematics, South Asian University, Delhi, 110021, India

    Kapil K. Sharma

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  1. Ram Prasad Yadav
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  2. Pratima Rai
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  3. Kapil K. Sharma
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Correspondence to Pratima Rai.

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Yadav, R.P., Rai, P. & Sharma, K.K. Non-Symmetric Interior Penalty Galerkin Finite Element Method for a Class of Singularly Perturbed Reaction Diffusion Problems with Discontinuous Data. Int. J. Appl. Comput. Math 8, 272 (2022). https://doi.org/10.1007/s40819-022-01467-2

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