ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF THE FIRST EIGENPAIR ASSOCIATED WITH p-LAPLACIAN

Guanglian Li; Jing Li; Julie Merten; Yifeng Xu; Shengfeng Zhu

doi:10.1137/24M1637052

ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF THE FIRST EIGENPAIR ASSOCIATED WITH p-LAPLACIAN

Guanglian Li
, Jing Li
, Julie Merten
, Yifeng Xu^*
, Shengfeng Zhu

^*Corresponding author for this work

School of Mathematical Sciences

Department of Mathematics
The University of Hong Kong
School Of Mathematical Science
East China Normal University
Computational and Numerical Mathematics
University of Groningen
Department of Mathematics
Shanghai Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper, we propose an adaptive finite element method for computing the first eigenpair of the p-Laplacian problem. We prove that by starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous problem, and the distance between discrete eigenfunctions and the normalized eigenfunction set corresponding to the first eigenvalue in W^1,p-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.

Original language	English
Pages (from-to)	A374-A402
Journal	SIAM Journal on Scientific Computing
Volume	47
Issue number	1
DOIs	https://doi.org/10.1137/24M1637052
State	Published - 2025

Keywords

a posteriori error estimator
adaptive finite element method
convergence
first eigenvalue
p-Laplacian

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10.1137/24M1637052

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title = "ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF THE FIRST EIGENPAIR ASSOCIATED WITH p-LAPLACIAN",

abstract = "In this paper, we propose an adaptive finite element method for computing the first eigenpair of the p-Laplacian problem. We prove that by starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous problem, and the distance between discrete eigenfunctions and the normalized eigenfunction set corresponding to the first eigenvalue in W1,p-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.",

keywords = "a posteriori error estimator, adaptive finite element method, convergence, first eigenvalue, p-Laplacian",

author = "Guanglian Li and Jing Li and Julie Merten and Yifeng Xu and Shengfeng Zhu",

year = "2025",

doi = "10.1137/24M1637052",

language = "英语",

volume = "47",

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T1 - ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF THE FIRST EIGENPAIR ASSOCIATED WITH p-LAPLACIAN

AU - Li, Guanglian

AU - Li, Jing

AU - Merten, Julie

AU - Xu, Yifeng

AU - Zhu, Shengfeng

PY - 2025

Y1 - 2025

N2 - In this paper, we propose an adaptive finite element method for computing the first eigenpair of the p-Laplacian problem. We prove that by starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous problem, and the distance between discrete eigenfunctions and the normalized eigenfunction set corresponding to the first eigenvalue in W1,p-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.

AB - In this paper, we propose an adaptive finite element method for computing the first eigenpair of the p-Laplacian problem. We prove that by starting from a fine initial mesh our proposed adaptive algorithm produces a sequence of discrete first eigenvalues that converges to the first eigenvalue of the continuous problem, and the distance between discrete eigenfunctions and the normalized eigenfunction set corresponding to the first eigenvalue in W1,p-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.

KW - a posteriori error estimator

KW - adaptive finite element method

KW - convergence

KW - first eigenvalue

KW - p-Laplacian

UR - https://www.scopus.com/pages/publications/85217885287

U2 - 10.1137/24M1637052

DO - 10.1137/24M1637052

M3 - 文章

AN - SCOPUS:85217885287

SN - 1064-8275

VL - 47

SP - A374-A402

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 1

ER -

ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF THE FIRST EIGENPAIR ASSOCIATED WITH p-LAPLACIAN

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Keywords

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