A Two-grid Semi-discretization For The Time-dependent Schr(?)dinger Equation

We firstly introduce the relevant background of the two-grid method and the Schrodinger equation in this dissertation.Then we give a review of the results made by many researchers.In the second chapter,to a kind of the time-dependent Schrodinger equation,we use the finite element method to construct a two-grid algorithm in the semi-discrete form.In the third chapter,we have a strictly theoretical analysis to the algorithm and prove that the semi-discrete solution has the same error order with the solution solved by the standard finite element method under‖·‖₁-norm.Finally,we summarize the dissertation and make a prospect to the future work.