Efficient Galerkin finite element methods for a time-fractional Cattaneo equation

In this paper, we develop two efficient fully discrete schemes for solving the time-fractional Cattaneo equation, where the fractional derivative is in the Caputo sense with order in $(1, 2]$ ( 1 , 2 ] . The schemes are based on the Galerkin finite element method in space and convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates are established with respect to data regularity. We further compare our schemes with the L2-$1_{\sigma }$ 1 σ scheme. Numerical examples are provided to show the efficiency of the schemes.