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A Dimensional-Splitting Weak Galerkin Finite Element Method for 2D Time-Fractional Diffusion Equation

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Abstract

In this article, the weak Galerkin finite element method, coupled with an operator-splitting method or known as dimensional-splitting technique, is proposed to solve a class of 2D time-fractional diffusion equation of order \(\beta \), \(0<\beta <1\) numerically. The time-fractional term is discretized using the well-known non-uniform L1-method, as the integer-order temporal derivatives of the solution blow up at the initial point. For the spatial discretization, a dimensional-splitting weak Galerkin finite element method is used in both x and y directions over a uniform mesh. The stability and the optimal error estimate of the proposed scheme are addressed in the \(L^2\)-norm. Finally, we present a numerical experiment to demonstrate the suitability of the stated method.

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Acknowledgements

The first author would like to express the thanks to Indian Institute of Technology Guwahati, India for funding of this project. The authors wish to acknowledge the anonymous referees for carefully reading the manuscript and providing their valuable comments and suggestions, which really helped to improve the presentation.

Funding

This work was supported by Indian Institute of Technology Guwahati, India.

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Authors and Affiliations

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

    Aniruddha Seal & Srinivasan Natesan

  2. Department of Computer Science, Faculty of Engineering, Artvin Çoruh University, 08100, Artvin, Turkey

    Suayip Toprakseven

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  1. Aniruddha Seal
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  2. Srinivasan Natesan
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  3. Suayip Toprakseven
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All authors contributed equally with respect to all aspects to this work.

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Correspondence to Srinivasan Natesan.

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Seal, A., Natesan, S. & Toprakseven, S. A Dimensional-Splitting Weak Galerkin Finite Element Method for 2D Time-Fractional Diffusion Equation. J Sci Comput 98, 56 (2024). https://doi.org/10.1007/s10915-023-02448-3

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  • DOI: https://doi.org/10.1007/s10915-023-02448-3

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