Convergence Analysis of Virtual Element Method for Nonlinear Nonlocal Dynamic Plate Equation

In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose C 1 conforming virtual element method (VEM) of arbitrary order, k ≥ 2 , to approximate the model problem numerically. We empl...

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Bibliographic Details
Published inJournal of scientific computing Vol. 91; no. 1; p. 23
Main Authors Adak, D., Mora, D., Natarajan, S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2022
Springer Nature B.V
Subjects
Algorithms
Computational Mathematics and Numerical Analysis
Convergence
Eigenvalues
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical functions
Mathematics
Mathematics and Statistics
Physical properties
Rectangular plates
Theoretical
Time dependence
65N15
Error estimates
65N12
74K20
Fourth order plate equation
Time dependent problem
35Q74
Virtual element method
65N30
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Summary:In this article, we have considered a nonlinear nonlocal time dependent fourth order equation demonstrating the deformation of a thin and narrow rectangular plate. We propose C 1 conforming virtual element method (VEM) of arbitrary order, k ≥ 2 , to approximate the model problem numerically. We employ VEM to discretize the space variable and fully implicit scheme for temporal variable. Well-posedness of the fully discrete scheme is proved under certain conditions on the physical parameters, and we derive optimal order of convergence in both space and time variable. Finally, numerical experiments are presented to illustrate the behaviour of the proposed numerical scheme.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01794-y