A Two-Scale Higher-Order Finite Element Discretization for Schrödinger Equation (Journal of Computational Mathematics, 2018)
In this paper, a two-scale higher-order finite element discretization scheme is proposedand analyzed for a Schrödinger equation on tensor product domains. With the scheme, thesolution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problemon a much coarser grid together with some eigenvalue problems on partially fine grids. Itis shown theoretically and numerically that the proposed two-scale higher-order schemenot only significantly reduces the number of degrees of freedom but also produces veryaccurate approximations.