Finite Difference Method for Nonlinear Damped Viscoelastic Euler‐Bernoulli Beam Model

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 stability and error estimate of the numerical solutions are derived for both the semi‐discrete‐in‐space scheme and the fully discrete scheme by the energy argument. 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.