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Volume 18, Issue 6
Energy and Mass Conservative Averaging Local Discontinuous Galerkin Method for Schrödinger Equation

Fubiao Lin, Yaxiang Li & Jun Zhang

Int. J. Numer. Anal. Mod., 18 (2021), pp. 723-739.

Published online: 2021-11

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  • Abstract

In this article, we develop the semi-discrete and fully discrete averaging local discontinuous Galerkin method to solve the well-known Schrödinger equation, in which space is discretized by the averaging local discontinuous Galerkin (ADG) method, and the time is discretized by Crank-Nicolson approach. Energy and mass conservative property of both schemes are proved. These schemes are shown to be unconditionally energy stable, and the error estimates are rigorously proved. Some numerical examples are performed to demonstrate the accuracy numerically.

  • Keywords

Averaging local discontinuous Galerkin method, Schrödinger equation, energy conservative, mass conservative, error analysis.

  • AMS Subject Headings

65L10, 34B27, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-723, author = {Lin , FubiaoLi , Yaxiang and Zhang , Jun}, title = {Energy and Mass Conservative Averaging Local Discontinuous Galerkin Method for Schrödinger Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {6}, pages = {723--739}, abstract = {

In this article, we develop the semi-discrete and fully discrete averaging local discontinuous Galerkin method to solve the well-known Schrödinger equation, in which space is discretized by the averaging local discontinuous Galerkin (ADG) method, and the time is discretized by Crank-Nicolson approach. Energy and mass conservative property of both schemes are proved. These schemes are shown to be unconditionally energy stable, and the error estimates are rigorously proved. Some numerical examples are performed to demonstrate the accuracy numerically.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19947.html} }
TY - JOUR T1 - Energy and Mass Conservative Averaging Local Discontinuous Galerkin Method for Schrödinger Equation AU - Lin , Fubiao AU - Li , Yaxiang AU - Zhang , Jun JO - International Journal of Numerical Analysis and Modeling VL - 6 SP - 723 EP - 739 PY - 2021 DA - 2021/11 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19947.html KW - Averaging local discontinuous Galerkin method, Schrödinger equation, energy conservative, mass conservative, error analysis. AB -

In this article, we develop the semi-discrete and fully discrete averaging local discontinuous Galerkin method to solve the well-known Schrödinger equation, in which space is discretized by the averaging local discontinuous Galerkin (ADG) method, and the time is discretized by Crank-Nicolson approach. Energy and mass conservative property of both schemes are proved. These schemes are shown to be unconditionally energy stable, and the error estimates are rigorously proved. Some numerical examples are performed to demonstrate the accuracy numerically.

Lin , FubiaoLi , Yaxiang and Zhang , Jun. (2021). Energy and Mass Conservative Averaging Local Discontinuous Galerkin Method for Schrödinger Equation. International Journal of Numerical Analysis and Modeling. 18 (6). 723-739. doi:
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