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Investigation of heat transport equation at the microscale via interpolating element-free Galerkin method

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Abstract

The current paper concerns to develop a new meshless numerical procedure to solve heat transport equation. For this aim, the Crank–Nicolson finite difference idea is used to discrete the time derivative. Thus, a time-discrete scheme is derived. The unconditional stability and convergence of the time-discrete scheme are proved by energy method. Then, the interpolating element-free Galerkin method is applied to get a full-discrete scheme. Furthermore, the convergence rate of the full-discrete formulation is studied. At the end, some examples are considered to compare the theoretical results with the computational results and also to show the efficiency and ability of the proposed numerical procedure.

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Acknowledgements

We would like to appreciate reviewers for their beneficial comments and suggestions that have improved our paper.

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

    Mostafa Abbaszadeh & Mehdi Dehghan

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  1. Mostafa Abbaszadeh
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  2. Mehdi Dehghan
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Correspondence to Mostafa Abbaszadeh.

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Abbaszadeh, M., Dehghan, M. Investigation of heat transport equation at the microscale via interpolating element-free Galerkin method. Engineering with Computers 38 (Suppl 4), 3317–3333 (2022). https://doi.org/10.1007/s00366-021-01425-4

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  • DOI: https://doi.org/10.1007/s00366-021-01425-4

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