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 - <p style="text-align: justify;">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.</p>