Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations

In this paper, a linearized L1Galerkin finite element method is proposed to solve the multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal-spatial error splitting argument, we prove that the finite element approximations in the L^2norm and L^\inftynorm are bounded without any time-step size conditions. More importantly, by using a discrete fractional Gronwall-type inequality, optimal error estimates of...