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Volume 27, Issue 2-3
A Two-Scale Higher-Order Finite Element Discretization for Schrödinger Equation

Huajie Chen, Fang Liu & Aihui Zhou

J. Comp. Math., 27 (2009), pp. 315-337.

Published online: 2009-04

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  • Abstract

In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schrödinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.

  • Keywords

Higher-order, Finite element, Discretization, Eigenvalue, Schrödinger equation, Two-scale.

  • AMS Subject Headings

65N15, 65N25, 65N30, 65N50, 65Y10.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-315, author = {Huajie Chen, Fang Liu and Aihui Zhou}, title = {A Two-Scale Higher-Order Finite Element Discretization for Schrödinger Equation}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {315--337}, abstract = {

In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schrödinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8575.html} }
TY - JOUR T1 - A Two-Scale Higher-Order Finite Element Discretization for Schrödinger Equation AU - Huajie Chen, Fang Liu & Aihui Zhou JO - Journal of Computational Mathematics VL - 2-3 SP - 315 EP - 337 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8575.html KW - Higher-order, Finite element, Discretization, Eigenvalue, Schrödinger equation, Two-scale. AB -

In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schrödinger equation on tensor product domains. With the scheme, the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids. It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.

Huajie Chen, Fang Liu and Aihui Zhou. (2009). A Two-Scale Higher-Order Finite Element Discretization for Schrödinger Equation. Journal of Computational Mathematics. 27 (2-3). 315-337. doi:
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