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A comparative study on interior penalty discontinuous Galerkin and enriched Galerkin methods for time-fractional Sobolev equation

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Abstract

This study documents the development of a novel scheme for spatial discretization of the time-fractional Sobolev equation. The scheme is based on a combination of continuous and discontinuous Galerkin methods which is called the enriched Galerkin method. The enriched Galerkin method has more degrees of freedom than the continuous Galerkin but smaller than the discontinuous Galerkin method. Also, the Caputo-type fractional operator is considered for fractional-order derivatives. Furthermore, unconditionally stability of the method is proved and a priori error estimate for the approximation is presented. Finally, we present several numerical examples to confirm the analytical results.

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Acknowledgements

The authors would like to express their deep thanks to anonymous referees for their careful reading and invaluable suggestions on this manuscript.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., 15914, Tehran, Iran

    Hadi Mohammadi-Firouzjaei, Hojatollah Adibi & Mehdi Dehghan

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  1. Hadi Mohammadi-Firouzjaei
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  2. Hojatollah Adibi
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  3. Mehdi Dehghan
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Correspondence to Hojatollah Adibi.

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Mohammadi-Firouzjaei, H., Adibi, H. & Dehghan, M. A comparative study on interior penalty discontinuous Galerkin and enriched Galerkin methods for time-fractional Sobolev equation. Engineering with Computers 38, 5379–5394 (2022). https://doi.org/10.1007/s00366-022-01624-7

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