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- Title
Two‐grid mixed finite element method for two‐dimensional time‐dependent Schrödinger equation.
- Authors
Tian, Zhikun; Chen, Yanping; Huang, Yunqing; Wang, Jianyun
- Abstract
In this paper, we study the semidiscrete mixed finite element scheme and construct a two‐grid algorithm for the two‐dimensional time‐dependent Schrödinger equation. We analyze error results of the mixed finite element solution in L2$$ {L}^2 $$‐norm by some projection operators. Then, we propose a two‐grid method of the semidiscrete mixed finite element. With this method, the solution of the Schrödinger equation on a fine grid is reduced to the solution of original problem on a much coarser grid together with the solution of two elliptic equations on the fine grid. We also obtain the error estimate of two‐grid solution with exact solution in L2$$ {L}^2 $$‐norm. Finally, a numerical experiment indicates that our two‐grid algorithm is more efficient than the standard mixed finite element method.
- Subjects
TIME-dependent Schrodinger equations; FINITE element method; ELLIPTIC equations
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 12, p12759
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9210