Application of finite-element method to the two-dimensional Schrödinger equation

1988 ◽  
Vol 9 (3) ◽  
pp. 222-231 ◽  
Author(s):  
Nobuyuki Sato ◽  
Suehiro Iwata
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Element Method

Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation

2013 ◽  
Vol 5 (2) ◽  
pp. 180-193 ◽  
Author(s):  
Hongmei Zhang ◽  
Jicheng Jin ◽  
Jianyun Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
Two Dimensional ◽  
Optimal Convergence ◽  
Standard Finite Element Method ◽  
Finite Element Schemes ◽  
Element Method

AbstractIn this paper, we construct semi-discrete two-grid finite element schemes and full-discrete two-grid finite element schemes for the two-dimensional time-dependent Schrödinger equation. The semi-discrete schemes are proved to be convergent with an optimal convergence order and the full-discrete schemes, verified by a numerical example, work well and are more efficient than the standard finite element method.

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