Two-grid methods for a class of nonlinear elliptic eigenvalue problems

被引:14
作者
Cances, Eric [1 ,2 ]
Chakir, Rachida [3 ]
He, Lianhua [4 ]
Maday, Yvon [4 ,5 ,6 ]
机构
[1] Univ Paris Est, CERMICS, Ecole Ponts, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee, France
[2] INRIA, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee, France
[3] Univ Paris Est, IFSTTAR, 14-20 Bd Newton, F-77447 Champs Sur Marne, Marne La Vallee, France
[4] UPMC Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France
[5] Inst Univ France, Paris, France
[6] Brown Univ, Div Appl Math, Providence, RI 02912 USA
关键词
nonlinear eigenvalue problem; spectral and pseudo spectral approximation; finite element approximation; ground state computation; numerical analysis; two-grid method; FINITE-DIMENSIONAL APPROXIMATIONS; NUMERICAL-ANALYSIS; DISCRETIZATION;
D O I
10.1093/imanum/drw053
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we introduce and analyse some two-grid methods for nonlinear elliptic eigenvalue problems of the form -div(D del u) + Vu + f (u(2))u = lambda u, parallel to u parallel to(L2) = 1. We provide a priori error estimates for the ground state energy, the eigenvalue lambda and the eigenfunction u, in various Sobolev norms. We focus in particular on the Fourier spectral approximation (for periodic boundary conditions), and on the P-1 and P-2 finite element discretizations (for homogeneous Dirichlet boundary conditions), taking numerical integration errors into account. Finally, we provide numerical examples illustrating our analysis.
引用
收藏
页码:605 / 645
页数:41
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