A Finite Element Approach to a Class of Fractional Wave Equations

This paper is concerned with a class of nonlinear time fractional wave equations. The fully discrete scheme is established by using fast L2-1 _\sigma formulas combined with the finite element method. The unconditional convergence property in H¹-norm of the scheme is proved by using the time-space splitting technique. Lastly, a series of numerical tests is carried out to validate the theoretical findings.