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 - <p style="text-align: justify;">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.</p>