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An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection–Diffusion PDEs

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Abstract

This article deals with the residual-based a posteriori error estimation in the standard energy norm for the streamline-diffusion finite element method (SDFEM) for singularly perturbed convection–diffusion equations. The well-known dual-weighted residual (DWR) technique has been adopted to elevate the accuracy of the error estimator. Our main contribution is finding an efficient computable DWR-type robust residual-based a posteriori error bound for the SDFEM. The local lower error bound has also been provided. An adaptive mesh refinement algorithm has been addressed and lastly, some numerical experiments are carried out to justify the theoretical proofs.

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Acknowledgements

The authors wish to acknowledge the referees for their valuable comments and suggestions, which helped to improve the presentation.

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  1. Department of Mathematics, Indian Institute of Technology, 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. An Efficient DWR-Type a Posteriori Error Bound of SDFEM for Singularly Perturbed Convection–Diffusion PDEs. J Sci Comput 90, 73 (2022). https://doi.org/10.1007/s10915-021-01749-9

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  • DOI: https://doi.org/10.1007/s10915-021-01749-9

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