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A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model

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Abstract

In this paper, we study the solute transport in heterogeneous media described by the time-fractional mobile/immobile advection diffusion model, where the integer and the fractional time derivatives are employed to characterize the movement of the particles in the mobile and immobile zone, respectively. We propose a fully discrete characteristic finite element scheme for the model, in which the modified method of characteristics is applied to handle the domination of advection. The optimal L2 error estimate is derived with first-order accuracy in time and second-order accuracy in space. Several practical numerical experiments are presented to validate the effectiveness and accuracy of the proposed method.

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Acknowledgements

The authors would like to express their most sincere thanks to the referees for their very helpful comments and suggestions, which greatly improved the quality of this paper.

Funding

The work is supported by the National Natural Science Foundation of China (Grant Nos. 11771375 and 91630207), Shandong Province Natural Science Foundation (Grant No. ZR2018MA008), Taishan Scholars Program of Shandong Province of China, OSD/ARO MURI Grant W911NF-15-1-0562, the National Science Foundation (Grant Nos. DMS-1620194, DMS-2012291), the China Postdoctoral Science Foundation (Grant No. 2020M681136), and the SPARC Graduate Research Grant from the Office of the Vice President for Research at the University of South Carolina.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Huan Liu

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xiangcheng Zheng

  3. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, China

    Chuanjun Chen

  4. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Hong Wang

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  1. Huan Liu
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  2. Xiangcheng Zheng
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  3. Chuanjun Chen
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  4. Hong Wang
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Correspondence to Chuanjun Chen.

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Communicated by: Martin Stynes

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Liu, H., Zheng, X., Chen, C. et al. A characteristic finite element method for the time-fractional mobile/immobile advection diffusion model. Adv Comput Math 47, 41 (2021). https://doi.org/10.1007/s10444-021-09867-6

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