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

• 来源期刊: 计算数学（英文版）
• 关键词: Higher-order Finite element Discretization Eigenvalue Schr(o)dinger equation Two-scale
• 年，卷（期）: 2009,（2）
• 页码范围: 315-337
• 页数: 23页
• 语种: 英文

摘要

In this paper,a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schr(o)dinger 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.