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

Jicheng Jin*, Xiaonan WU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)777-793
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number3
DOIs
Publication statusPublished - 1 Jun 2010

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Artificial boundary condition
  • Finite element method
  • Schrödinger equation

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