Applied Mathematics and Mechanics

, Volume 39, Issue 9, pp 1353–1372 | Cite as

Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

  • Jianyun Wang
  • Yanping ChenEmail author


Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schrödinger equation with the finite element method. The error estimate and superconvergence property with order O(hk+1) in the H1 norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(hk+1 + τ2) in the H1 norm can be obtained in the Crank-Nicolson fully discrete scheme.

Key words

superconvergence elliptic projection Schrödinger equation interpolation post-processing 

Chinese Library Classification


2010 Mathematics Subject Classification

65M12 65M15 65M60 


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We would like to thank anonymous referees for their insightful comments that improved this paper.


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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ScienceHunan University of TechnologyZhuzhouChina
  2. 2.School of Mathematical SciencesSouth China Normal UniversityGuangzhouChina

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