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arXiv · 2505.02517

Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model

Wenlin Qiu·Xiangcheng Zheng·Tao Guo·Xu Xiao
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Abstract

We propose and analyze the numerical approximation for a viscoelastic Euler-Bernoulli beam model containing a nonlinear strong damping coefficient. The finite difference method is used for spatial discretization, while the backward Euler method and the averaged PI rule are applied for temporal discretization. The long-time stability and the finite-time error estimate of the numerical solutions are derived for both the semi-discrete-in-space scheme and the fully-discrete scheme. Furthermore, the Leray-Schauder theorem is used to derive the existence and uniqueness of the fully-discrete numerical solutions. Finally, the numerical results verify the theoretical analysis.

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Wenlin Qiu, Xiangcheng Zheng, Tao Guo, Xu Xiao. 2025-05-05. Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model. https://arxiv.org/abs/2505.02517

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