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Volume 5, Issue 2
Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation

Hongmei Zhang, Jicheng Jin & Jianyun Wang

Adv. Appl. Math. Mech., 5 (2013), pp. 180-193.

Published online: 2013-05

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  • Abstract

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.

  • Keywords

Schrödinger equation, two-grid method, finite element method.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-180, author = {Hongmei and Zhang and and 20153 and and Hongmei Zhang and Jicheng and Jin and and 20154 and and Jicheng Jin and Jianyun and Wang and and 20155 and and Jianyun Wang}, title = {Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {2}, pages = {180--193}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.12-m1206}, url = {http://global-sci.org/intro/article_detail/aamm/64.html} }
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.

Hongmei Zhang, Jicheng Jin & Jianyun Wang. (1970). Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation. Advances in Applied Mathematics and Mechanics. 5 (2). 180-193. doi:10.4208/aamm.12-m1206
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