A TWO-SCALE HIGHER-ORDER FINITE ELEMENT DISCRETIZATION FOR SCHRDINGER EQUATION  

作　　者：Huajie Chen Fang Liu Aihui Zhou 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China [2]Graduate University of Chinese Academy of Sciences, Beijing 100190, China [3]School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081, China

出　　处：《Journal of Computational Mathematics》2009年第2期315-337,共23页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China (10701083 and 10425105);the National Basic Research Program of China (2005CB321704).

摘　　要：In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger 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.In this paper, a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schroedinger 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.

关 键 词：HIGHER-ORDER Finite element DISCRETIZATION EIGENVALUE Schroedinger equation TWO-SCALE 

分 类 号：O413.1[理学—理论物理] TV662.2[理学—物理]