Department of Mathematics
Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip
This paper addresses the finite element method for the two-dimensional time-dependent Schrödinger equation on an infinite strip by using artificial boundary conditions. We first reduce the original problem into an initial-boundary value problem in a bounded domain by introducing a transparent boundary condition, then fully discretize this reduced problem by applying the Crank-Nicolson scheme in time and a bilinear or quadratic finite element approximation in space. This scheme, by a rigorous analysis, has been proved to be unconditionally stable and convergent, and its convergence order has also been obtained. Finally, two numerical examples are given to verify the accuracy of the scheme. © 2010 Elsevier B.V. All rights reserved.
Artificial boundary condition, Finite element method, Schrödinger equation
Source Publication Title
Journal of Computational and Applied Mathematics
Link to Publisher's Edition
Jin, J., & Wu, X. (2010). Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip. Journal of Computational and Applied Mathematics, 234 (3), 777-793. https://doi.org/10.1016/j.cam.2010.01.042