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Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation

Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation

Year:    2025

Author:    Jing Sun, Daxin Nie, Weihua Deng

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2206-m2022-0054

Journal of Computational Mathematics, Vol. 43 (2025), Iss. 2 : pp. 257–279

Published online:    2025-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

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

Author Details

Jing Sun

Daxin Nie

Weihua Deng