The virtual element method for a nonhomogeneous double obstacle problem of Kirchhoff plate. (June 2023)

• Record Type: Journal Article
• Authors: Feng, Fang; Huang, Jianguo
• Is Part Of: Nonlinear analysis. Volume 71(2023)
• Publication Date: 2023-06
• Subjects: Virtual element method -- Nonhomogeneous obstacle problem -- Error estimate -- The primal–dual active set algorithm; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103831
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is intended to propose and analyze the lowest order conforming and nonconforming virtual element methods (VEMs) for a nonhomogeneous double obstacle problem in fourth-order variational inequality. We first present an abstract framework for the error analysis of an abstract discrete method. Then, we develop the conforming and fully nonconforming VEMs for the previous problem, with the optimal error estimates obtained by using the previous abstract framework combined with two modified interpolation operators and the related estimates. The discrete problem is solved by the primal–dual active set algorithm and the numerical results are in good agreement with theoretical findings.