Regularity Theory and Numerical Algorithm for the Time-Fractional Klein-Kramers Equation (Journal of Computational Mathematics, 2024)
Fractional Klein-Kramers equation can well describe subdiffusion in phase space. Inthis paper, we develop the fully discrete scheme for time-fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local discontinuous Galerkinmethods. Thanks to the obtained sharp regularity estimates in temporal and spatial directions after overcoming the hypocoercivity of the operator, the complete error analysesof the fully discrete scheme are built. It is worth mentioning that the convergence of theprovided scheme is independent of the temporal regularity of the exact solution. Finally,numerical results are proposed to verify the correctness of the theoretical results.