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Mixed element algorithm based on a second-order time approximation scheme for a two-dimensional nonlinear time fractional coupled sub-diffusion model

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Abstract

In this article, a numerical algorithm is presented to solve a two-dimensional nonlinear time fractional coupled sub-diffusion problem, where the second-order Crank–Nicolson scheme with a second-order WSGD formula is used in the time direction, and a mixed element method is applied in the space direction. The existence and uniqueness of the mixed element solution and the stability for fully discrete scheme are proven. In addition, the optimal a priori error estimates for unknown scalar function u and v in \(L^2\) and \(H^1\)-norms and a priori error estimates for their fluxes \(\sigma\) and \(\lambda\) in \((L^2)^2\)-norm are obtained. Finally, some numerical calculations are presented to illustrate the validity for the proposed numerical algorithm.

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Acknowledgements

The authors are grateful to two referees and editor for their valuable suggestions which greatly improved the presentation of the paper. This work is supported by the National Natural Science Foundation of China (11661058, 11761053, 11701299), Natural Science Foundation of Inner Mongolia (2016MS0102, 2017MS0107), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (NJYT-17-A07).

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Authors and Affiliations

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    Ruihan Feng, Yang Liu, Yaxin Hou, Hong Li & Zhichao Fang

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  1. Ruihan Feng
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  2. Yang Liu
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  3. Yaxin Hou
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  4. Hong Li
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  5. Zhichao Fang
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Correspondence to Yang Liu.

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Feng, R., Liu, Y., Hou, Y. et al. Mixed element algorithm based on a second-order time approximation scheme for a two-dimensional nonlinear time fractional coupled sub-diffusion model. Engineering with Computers 38, 51–68 (2022). https://doi.org/10.1007/s00366-020-01032-9

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