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 $\alpha\in (1, 2)$ and $\beta\in(0, 1)$, 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.