In this paper, the Rayleigh beam system with two dynamical boundary controls is treated. Theoretically, the well-posedness of the weak solution is obtained. Later, we discretize the system by using the Implicit Euler scheme in time and the \(P^3\) Hermite finite element in space. In addition, we show the decay of the discrete energy and we establish some a priori error estimates. Finally, some numerical simulations are presented.

中文翻译：

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具有动态边界控制的瑞利梁方程的数值分析与仿真

本文研究了具有两个动态边界控制的瑞利光束系统。从理论上讲，获得了弱解的适定性。稍后，我们通过及时使用隐式Euler方案和空间中的\（P ^ 3 \） Hermite有限元来离散化系统。此外，我们显示了离散能量的衰减，并建立了一些先验误差估计。最后，给出了一些数值模拟。