Computing the First Eigenpair of the -Laplacian via Inverse Iteration of Sublinear Supersolutions

被引：25

作者：

Biezuner, Rodney Josue ^{[1
]}

Brown, Jed ^{[2
,3
]}

Ercole, Grey ^{[1
]}

Martins, Eder Marinho ^{[4
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat ICEx, BR-30161970 Belo Horizonte, MG, Brazil

[2] ETH, Lab Hydraul Hydrol & Glaciol VAW, CH-8092 Zurich, Switzerland

[3] Argonne Natl Lab, Math & Comp Sci Div, Argonne, IL 60439 USA

[4] Univ Fed Ouro Preto, Dept Matemat ICEB, BR-35400000 Ouro Preto, MG, Brazil

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2012年 / 52卷 / 01期

关键词：

p-Laplacian; First eigenvalue and eigenfunction; Inverse iteration; Lane-Emden problem; Torsional creep problem; FINITE-ELEMENT-METHOD; P-LAPLACIAN; ELLIPTIC-OPERATORS; POSITIVE SOLUTIONS; APPROXIMATION; EIGENVALUES; COMPUTATION; DIFFUSION; ALGORITHM; EQUATION;

D O I：

10.1007/s10915-011-9540-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce an iterative method for computing the first eigenpair ( , ) for the -Laplacian operator with homogeneous Dirichlet data as the limit of ( (,) ) as -> (-), where is the positive solution of the sublinear Lane-Emden equation with the same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of to is in the (1)-norm and the rate of convergence of to is at least (-). Numerical evidence is presented.

引用

页码：180 / 201

页数：22

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