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Hermite Finite Element Method for a Class of Viscoelastic Beam Vibration Problem
School of Mathematics and Statistics, Shandong Normal University, Jinan, China
School of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 1 School of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 2 School of Mathematics and Statistics, Shandong Normal University, Jinan, China
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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 L 2 -norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme.
KeywordsViscoelastic BeamHermite ElementError EstimateNumerical Simulation
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