TY - JOUR T1 - Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation AU - Zhang , Hongmei AU - Jin , Jicheng AU - Wang , Jianyun JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 180 EP - 193 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.12-m1206 UR - https://global-sci.org/intro/article_detail/aamm/64.html KW - Schrödinger equation, two-grid method, finite element method. AB -

In 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.