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

¹ College of Science, Guilin University of Technology, Guilin, Guangxi 541004, P.R. China.
² School of Sciences, Lanzhou University of Technology, Lanzhou, Gansu 730050, P.R. China.

^* Corresponding author: chena@glut.edu.cn

Received: 21 June 2020
Accepted: 22 January 2021

Abstract

In this paper, we consider a two-term time-fractional diffusion-wave equation which involves the fractional orders α ∈ (1, 2) and β ∈ (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.