TY - JOUR
T1 - Two-Grid Crank-Nicolson Finite Volume Element Method for the Time-Dependent Schrödinger Equation
AU - Chen , Chuanjun
AU - Lou , Yuzhi
AU - Zhang , Tong
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1357
EP - 1380
PY - 2022
DA - 2022/08
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0233
UR - https://global-sci.org/intro/article_detail/aamm/20851.html
KW - Finite volume element method, two-grid method, Crank-Nicolson scheme, error estimates, Schrödinger equation.
AB - <p style="text-align: justify;">In this paper, we construct a Crank-Nicolson finite volume element scheme
and a two-grid decoupling algorithm for solving the time-dependent Schrödinger equation. Combining the idea of two-grid discretization, the decoupling algorithm involves
solving a small coupling system on a coarse grid space and a decoupling system with
two independent Poisson problems on a fine grid space, which can ensure the accuracy
while the size of coarse grid is much coarser than that of fine grid. We further provide
the optimal error estimate of these two schemes rigorously by using elliptic projection
operator. Finally, numerical simulations are provided to verify the correctness of the
theoretical analysis.</p>