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A Mixed Finite Element Method for Solving the Time-Fractional-Darcy Equation

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Abstract

Darcy flow is an important mathematical model to describe a fluid through a porous media. Many research reveal fractional model is an alternative approach to simulate the porous medium flow. To seek more accurate mathematical model for this type of flow, a novel Time-Fractional-Darcy equation is investigated and numerically solved in this paper. The finite difference method is utilized to discrete the temporal fractional derivative. For pursuing higher calculate accuracy and better numerical stability, the fully coupled mixed finite element methods with stabilized terms are proposed in space. The effectiveness and accuracy of the presented methodology are consistently demonstrated by 2D and 3D numerical examples.

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Funding

This work was funded by Shenzhen Science and Technology Program of China under Grant RCBS202007414114939091, Guangdong Basic and Applied Basic Research Foundation of China under Grants 2022A1515110152 and 2023A1515010854.

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Authors and Affiliations

  1. Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, College of Civil Engineering, Huaqiao University, Xiamen, 361021, China

    Junchao Wu

  2. Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen, 518055, China

    Zeng Lin

Authors
  1. Junchao Wu
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  2. Zeng Lin
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Dr. Junchao Wu implemented the numerical simulation and Dr. Zeng Lin wrote the whole manuscript text.

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Correspondence to Zeng Lin.

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Wu, J., Lin, Z. A Mixed Finite Element Method for Solving the Time-Fractional-Darcy Equation. Int. J. Appl. Comput. Math 10, 66 (2024). https://doi.org/10.1007/s40819-024-01692-x

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