标题： 非线性阻尼粘弹性Euler-Bernoulli梁模型的有限差分法 显示英文标题

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

摘要： 我们提出并分析了一种粘弹性欧拉-伯努利梁模型的数值逼近，该模型包含一个非线性的强阻尼系数。空间离散化采用了有限差分法，而时间离散化则应用了向后欧拉法和平均PI规则。我们推导出了半离散空间格式和全离散格式下数值解的长时间稳定性及有限时间误差估计。此外，我们使用Leray-Schauder定理得出了全离散数值解的存在性和唯一性。最后，数值结果验证了理论分析。 显示英文摘要

摘要： 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.