Two-scale finite element discretizations for nonlinear eigenvalue problems in quantum physics

被引：0
|
作者：
Pengyu Hou
Fang Liu
机构：
[1] Beijing Normal University,School of Mathematical Sciences
[2] Central University of Finance and Economics,School of Statistics and Mathematics
来源：
Advances in Computational Mathematics | 2021年 / 47卷
关键词：
Nonlinear eigenvalue problem; Finite element; Two-scale; Discretization; 65N15; 65N30; 65N55; 65F10; 65Y10;
D O I：
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学科分类号：
摘要：
In this paper, some two-scale finite element discretizations are introduced and analyzed for a class of nonlinear elliptic eigenvalue problems on tensor product domains. It is shown that the solution obtained by the standard finite element method on a one-scale fine grid can be numerically replaced with a combination of some solutions on a coarse grid and some univariate fine grids by two-scale finite element discretizations. Compared with the standard finite element solution, the two-scale finite element approximations save computational cost significantly while achieving the same accuracy.
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