Year: 2022
Author: Chuanjun Chen, Yuzhi Lou, Tong Zhang
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 6 : pp. 1357–1380
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0233
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 6 : pp. 1357–1380
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Finite volume element method two-grid method Crank-Nicolson scheme error estimates Schrödinger equation.