Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910928171171840 |
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| author | Qiu, Wenlin Zheng, Xiangcheng Guo, Tao Xiao, Xu |
| author_facet | Qiu, Wenlin Zheng, Xiangcheng Guo, Tao Xiao, Xu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model Qiu, Wenlin Zheng, Xiangcheng Guo, Tao Xiao, Xu Numerical Analysis 35L75, 65M15, 65M22, 45K05 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. |
| title | Finite difference method for nonlinear damped viscoelastic Euler-Bernoulli beam model |
| topic | Numerical Analysis 35L75, 65M15, 65M22, 45K05 |
| url | https://arxiv.org/abs/2505.02517 |