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 - <p style="text-align: justify;">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.<br/></p>