Recovery-type A Posterior Error Estimation And Adaptive Algorithm Of Finite Element Method For Linear Schr(?)dinger Equation

In this thesis,We derive a posteriori error estimates for of linear Schr(?)dingertype equations.For the discretization in time we use the Crank-Nicolson method,while for the space discretization we use finite element spaces that are allowed to change in time.The derivation of the estimators is based on a elliptic reconstruction.The final estimates are obtained using energy techniques and recovery-type estimators.Then,two adaptive algorithms were designed based on the reconstructed posterior error estimation.Finally,the feasibility of the algorithm and the validity of the error estimator were verified by numerical examples,and the adaptive algorithm was applied on the solution to the nonlinear Schr(?)dinger equation.