Work

Adaptive Finite Element Approximations of the First Eigenpair Associated with \({p}\)-Laplacian

Year: 2025

Type: article

Abstract: . In this paper, we propose an adaptive finite element method for computing the first eigenpair of the [Formula: see text]-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 [Formula: see text]-norm also tends to zero. Extensive numerical examples are provided to show the effectiveness and efficiency.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/24m1637052

Authors: Guanglian Li, Jing Li, Julie Merten, Yifeng Xu, Shengfeng Zhu

Institutions: University of Hong Kong, East China Normal University, University of Groningen, Shanghai Normal University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Research Grants Council, University Grants Committee, Science and Technology Commission of Shanghai Municipality, General Research Fund of Shanghai Normal University