Error estimates for a robust finite element method of two-term time-fractional diffusion-wave equation with nonsmooth data

In this paper, we consider a two-term time-fractional diffusion-wave equation which involves the fractional orders alpha is an element of (1, 2) and beta is an element of (0, 1), respectively. By using piecewise linear Galerkin finite element method in space and convolution quadrature based on second-order backward difference method in time, we obtain a robust fully discrete scheme. Error estimates for semidiscrete and fully discrete schemes are established with respect to nonsmooth data. Numerical experiments for two-dimensional problems are provided to illustrate the efficiency of the method and conform the theoretical results.