2025/05/04 by Tao Guo, Yiqun Li, Guo, Tao +3
Engineering · Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2505.02132
openalex publication_date 2025/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the numerical approximation to the Euler-Bernoulli (E-B) beams and plates with nonlinear nonlocal strong damping, which describes the damped mechanical behavior of beams and plates in real applications. We discretize the damping term by the composite Simpson's rule and the six-point Simpson's formula in the beam and plate problems, respectively, and then construct the fully discrete compact difference scheme for these problems. To account for the nonlinear-nonlocal term, we design several novel discrete norms to facilitate the error estimates of the damping term and the numerical scheme. The stability, convergence, and energy dissipation properties of the proposed scheme are proved, and numerical experiments are carried out to substantiate the theoretical findings.