Work

The interior penalty virtual element method for fourth-order singular perturbation problems

Year: 2023

Type: preprint

Abstract: This paper is dedicated to the numerical solution of a fourth-order singular perturbation problem using the interior penalty virtual element method (IPVEM) proposed in [42]. The study introduces modifications to the jumps and averages in the penalty term, as well as presents an automated mesh-dependent selection of the penalty parameter. Drawing inspiration from the modified Morley finite element methods, we leverage the conforming interpolation technique to handle the lower part of the bilinear form. Through our analysis, we establish optimal convergence in the energy norm and provide a rigorous proof of uniform convergence concerning the perturbation parameter in the lowest-order case.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2312.10860

Authors: Feng, Fang, Yu, Yue

Institutions: Nanjing University of Science and Technology, Xiangtan University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

OpenAlex ID: W4389983992

Cites:

Cited by: 1

Related to: 10