A Finite Element Method For Schr(?)dinger Equation With Neumann Boundary Conditions In An Unbounded Strip

This thesis mainly discusses the finite element method for Schro¨dinger equation withNeumann boundary condition in an unbounded strip. First, we reduce the original prob-lem into an initial-boundary value problem in a bounded domain by introducing an artificialboundary condition, and then fully discrete this problem by applying Crank-Nicolson schemein time and linear or quadratic finite element approximation in space. By a rigorous analysis,this scheme has been proved to be unconditionally stable and convergent, and its convergenceorder has also been obtained. Finally, we give a numerical example to verify the accuracy ofthe scheme.