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Volume 33, Issue 2
A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation

Jicheng Jin, Ning Wei & Hongmei Zhang

DOI: 10.4208/jcm.1409-m4323

J. Comp. Math., 33 (2015), pp. 146-157.

Published online: 2015-04

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  • Abstract

In this paper, some two-grid finite element schemes are constructed for solving the nonlinear Schrödinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.

  • Keywords

Nonlinear Schrödinger equation, Finite element method, Two-grid

  • AMS Subject Headings

65N30, 65N55.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jcjin2008@sina.com (Jicheng Jin)

weiningjiayou@126.com (Ning Wei)

  • BibTex
  • RIS
  • TXT
@Article{JCM-33-146, author = {Jin , JichengWei , Ning and Zhang , Hongmei}, title = {A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {2}, pages = {146--157}, abstract = {

In this paper, some two-grid finite element schemes are constructed for solving the nonlinear Schrödinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1409-m4323}, url = {http://global-sci.org/intro/article_detail/jcm/9833.html} }
TY - JOUR T1 - A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation AU - Jin , Jicheng AU - Wei , Ning AU - Zhang , Hongmei JO - Journal of Computational Mathematics VL - 2 SP - 146 EP - 157 PY - 2015 DA - 2015/04 SN - 33 DO - http://doi.org/10.4208/jcm.1409-m4323 UR - https://global-sci.org/intro/article_detail/jcm/9833.html KW - Nonlinear Schrödinger equation, Finite element method, Two-grid AB -

In this paper, some two-grid finite element schemes are constructed for solving the nonlinear Schrödinger equation. With these schemes, the solution of the original problem is reduced to the solution of the same problem on a much coarser grid together with the solutions of two linear problems on a fine grid. We have shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy.

Jicheng Jin, Ning Wei & Hongmei Zhang. (2020). A Two-Grid Finite-Element Method for the Nonlinear Schrödinger Equation. Journal of Computational Mathematics. 33 (2). 146-157. doi:10.4208/jcm.1409-m4323
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