A fast linearized Galerkin finite element method for the nonlinear multi-term time fractional wave equation

Abstract

This paper is concerned with a class of nonlinear multi-term time fractional wave equations. Based on the Galerkin finite element method (FEM) in space and the L2-1σ formula in time, combined with the corresponding fast algorithm, an efficient fully discrete scheme is constructed. The unconditional optimal convergence property in H1-norm of the proposed scheme is discussed by utilizing the time-space splitting technique. Furthermore, the optimal L2-norm convergence and the H1-norm superconvergence results of the method are obtained. Finally, several illustrative numerical experiments are performed to verify the theoretical results. Compared with the existing works, studying the convergence of FEMs for the nonlinear fractional wave equation is a great challenging task, and there are significant differences in research approaches.