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

2025/05/05 by Wenlin Qiu, Qiu, Wenlin, Xiangcheng Zheng +5
Chemical Engineering · Computer Science · Engineering · #35L75 #45K05 #65M15 #65M22 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies #Vibration and Dynamic Analysis

paper · pdf · doi:10.48550/arxiv.2505.02517

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping
• Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
• A Priori hp-estimates for Discontinuous Galerkin Approximations to\n Linear Hyperbolic Integro-Differential Equations
• Continuous Galerkin finite element methods for hyperbolic\n integro-differential equations

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