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 Schrodinger 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

Schrodinger 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 Zhang, Jicheng Jin 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 Schrodinger 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 - Hongmei Zhang, Jicheng Jin & Jianyun Wang JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 180 EP - 193 PY - 2013 DA - 2013/05 SN - 5 DO - http://dor.org/10.4208/aamm.12-m1206 UR - https://global-sci.org/intro/article_detail/aamm/64.html KW - Schrodinger equation KW - two-grid method KW - 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 Schrodinger 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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