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A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives

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Abstract

Our main aim in the current paper is to find a numerical plan for 2D Rayleigh–Stokes model with fractional derivative on irregular domains such as circular, L-shaped and a unit square with a circular and square hole. The employed fractional derivative is the Riemann–Liouville sense. Also, by integrating the equation corresponding to the time variable and then using the Galerkin FEM for the space direction, we obtain a full discrete scheme. The unconditional stability and the convergence estimate of the new scheme have been concluded. Finally, we evaluate results of Galerkin FEM with other numerical methods.

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Acknowledgments

We are immensely grateful to both reviewers for their comments on an earlier version of the manuscript.

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

    Mehdi Dehghan & Mostafa Abbaszadeh

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

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Dehghan, M., Abbaszadeh, M. A finite element method for the numerical solution of Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivatives. Engineering with Computers 33, 587–605 (2017). https://doi.org/10.1007/s00366-016-0491-9

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