TITLE:
Hermite Finite Element Method for a Class of Viscoelastic Beam Vibration Problem
AUTHORS:
Ying Tang, Zhe Yin
KEYWORDS:
Viscoelastic Beam, Hermite Element, Error Estimate, Numerical Simulation
JOURNAL NAME:
Engineering,
Vol.13 No.8,
August
20,
2021
ABSTRACT: Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge construction, aerospace and other fields. It has important engineering practice value and scientific significance for the design of numerical schemes. In this paper, a scheme for vibration equation of viscoelastic beam is developed by using the Hermite finite element. Based on an elliptic projection, the errors of semi-discrete scheme and fully discrete scheme are analyzed respectively, and the optimal L2-norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme.