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Volume 43, Issue 2
Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation

Jing Sun, Daxin Nie & Weihua Deng

DOI: 10.4208/jcm.2206-m2022-0054

J. Comp. Math., 43 (2025), pp. 257-279.

Published online: 2024-11

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  • Abstract

Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin methods. Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator, the complete error analyses of the fully discrete scheme are built. It is worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact solution. Finally, numerical results are proposed to verify the correctness of the theoretical results.

  • Keywords

Time-fractional Klein-Kramers equation, Regularity estimate, Convolution quadrature, Local discontinuous Galerkin method, Error analysis.

  • AMS Subject Headings

65M60, 35R11, 65M12, 65M15

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-43-257, author = {Sun , JingNie , Daxin and Deng , Weihua}, title = {Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {43}, number = {2}, pages = {257--279}, abstract = {

Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin methods. Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator, the complete error analyses of the fully discrete scheme are built. It is worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact solution. Finally, numerical results are proposed to verify the correctness of the theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2206-m2022-0054}, url = {http://global-sci.org/intro/article_detail/jcm/23538.html} }
TY - JOUR T1 - Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation AU - Sun , Jing AU - Nie , Daxin AU - Deng , Weihua JO - Journal of Computational Mathematics VL - 2 SP - 257 EP - 279 PY - 2024 DA - 2024/11 SN - 43 DO - http://doi.org/10.4208/jcm.2206-m2022-0054 UR - https://global-sci.org/intro/article_detail/jcm/23538.html KW - Time-fractional Klein-Kramers equation, Regularity estimate, Convolution quadrature, Local discontinuous Galerkin method, Error analysis. AB -

Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkin methods. Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator, the complete error analyses of the fully discrete scheme are built. It is worth mentioning that the convergence of the provided scheme is independent of the temporal regularity of the exact solution. Finally, numerical results are proposed to verify the correctness of the theoretical results.

Sun , JingNie , Daxin and Deng , Weihua. (2024). Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation. Journal of Computational Mathematics. 43 (2). 257-279. doi:10.4208/jcm.2206-m2022-0054
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