Linearized Transformed L1 Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schr?dinger Equations

A linearized transformed L1 Galerkin finite element method (FEM) is pre-sented for numerically solving the multi-dimensional time fractional Schrodinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gronwall inequality, the corresponding Sobolev embedding theorems and some in-verse inequalities. While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches. Numerical exam-ples are presented to confirm the theoretical results.