Abstract
In this paper, we analyze a space-time finite element method for fractional wave problems involving the time fractional derivative of order γ (1 < γ < 2). We first establish the stability of the proposed method and then derive the optimal convergence rate in H1(0,T;L2(Ω))-norm and suboptimal rate in discrete $ L^{\infty }(0,T;{H_{0}^{1}}({\Omega })) $ -norm. Furthermore, we discuss the performance of this method when the true solution has singularity at t = 0 and show that optimal convergence rate with respect to H1(0,T;L2(Ω))-norm can still be achieved by using graded temporal grids. Finally, numerical experiments are performed to verify the theoretical results.
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