A Nonconforming Virtual Element Method for a Fourth-order Hemivariational Inequality in Kirchhoff Plate Problem

This paper is devoted to a fourth-order hemivariational inequality for a Kirchhoff plate problem. A solution existence and uniqueness result is proved for the hemivariational inequality through the analysis of a corresponding minimization problem. A nonconforming virtual element method is developed...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 90; no. 3; p. 89
Main Authors: Feng, Fang, Han, Weimin, Huang, Jianguo
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2022
Springer Nature B.V
Subjects:
Algorithms
Banach spaces
Computational Mathematics and Numerical Analysis
Convergence
Convex analysis
Error analysis
Inequality
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Numerical analysis
Optimization
Theoretical
Nonconforming virtual element method
Hemivariational inequality
Error analysis
Kirchhoff plate problem
Double bundle algorithm
Well-posedness
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:This paper is devoted to a fourth-order hemivariational inequality for a Kirchhoff plate problem. A solution existence and uniqueness result is proved for the hemivariational inequality through the analysis of a corresponding minimization problem. A nonconforming virtual element method is developed to solve the hemivariational inequality. An optimal order error estimate in a broken H 2 -norm is derived for the virtual element solutions under appropriate solution regularity assumptions. The discrete problem can be formulated as an optimization problem for a difference of two convex (DC) functions and a convergent algorithm is used to solve it. Computer simulation results on a numerical example are reported, providing numerical convergence orders that match the theoretical prediction.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01759-1