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Numerical analysis and simulation for Rayleigh beam equation with dynamical boundary controls
Arabian Journal of Mathematics ( IF 0.9 ) Pub Date : 2021-02-15 , DOI: 10.1007/s40065-021-00310-8 Moussa Bzeih , Toufic El Arwadi , Mohammad Hindi
中文翻译:
具有动态边界控制的瑞利梁方程的数值分析与仿真
更新日期:2021-02-16
Arabian Journal of Mathematics ( IF 0.9 ) Pub Date : 2021-02-15 , DOI: 10.1007/s40065-021-00310-8 Moussa Bzeih , Toufic El Arwadi , Mohammad Hindi
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:
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。