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SDFEM for singularly perturbed parabolic initial-boundary-value problems on equidistributed grids

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Abstract

In this article, we study the convergence properties of the streamline-diffusion finite element method (SDFEM) for singularly perturbed 1D parabolic convection–diffusion initial-boundary-value problems. To discretize the spatial domain, we use a layer-adaptive nonuniform grids obtained through the equidistribution principle, whereas uniform grid is used in the time direction. Here, we use the backward-Euler method to discretize the temporal derivative and the SDFEM scheme for the spatial derivatives. The proposed method is uniformly convergent with first-order in time and second-order in space.

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Acknowledgements

The authors wish to acknowledge the referee for his valuable comments and suggestions, which really helped to improve the presentation. The first author would like to give thanks to the IIT Guwahati for supporting him financially in his research.

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

    D. Avijit & S. Natesan

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  1. D. Avijit
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  2. S. Natesan
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Correspondence to S. Natesan.

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Avijit, D., Natesan, S. SDFEM for singularly perturbed parabolic initial-boundary-value problems on equidistributed grids. Calcolo 57, 23 (2020). https://doi.org/10.1007/s10092-020-00375-5

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  • DOI: https://doi.org/10.1007/s10092-020-00375-5

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