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Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Convergence of a finite element scheme for the two-dimensional time-dependent Schrödinger equation in a long strip

Language

English

Abstract

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.

Keywords

Artificial boundary condition, Finite element method, Schrödinger equation

Publication Date

2010

Source Publication Title

Journal of Computational and Applied Mathematics

Volume

234

Issue

3

Start Page

777

End Page

793

Publisher

Elsevier

ISSN (print)

03770427

ISSN (electronic)

18791778

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