论文标题
带有p-biharmonic操作员的光束方程的混合有限元方法
Mixed finite element method for a beam equation with the p-biharmonic operator
论文作者
论文摘要
在本文中，我们考虑使用P-Biharmonic操作员的非线性束方程，其中$ 1 <p <\ infty $。使用变量的更改，我们将问题转换为微分方程系统，并通过应用Lax-Milgram定理和功能分析的经典结果来证明弱解决方案的存在，独特性和规律性。我们研究了该系统的离散公式，并在Brouwer定理的帮助下，我们表明该问题具有离散解决方案。离散解决方案的独特性和稳定性是通过经典方法获得的。建立收敛顺序后，我们应用混合有限元方法来获得方程代数系统。最后，我们在MATLAB软件中实现了计算代码，并在理论和仿真之间进行比较。
In this paper, we consider a nonlinear beam equation with the p-biharmonic operator, where $1 < p < \infty$. Using a change of variable, we transform the problem into a system of differential equations and prove the existence, uniqueness and regularity of the weak solution by applying the Lax-Milgram theorem and classical results of functional analysis. We investigate the discrete formulation for that system and, with the aid of the Brouwer theorem, we show that the problem has a discrete solution. The uniqueness and stability of the discrete solution are obtained through classical methods. After establishing the order of convergence, we apply the mixed finite element method to obtain an algebraic system of equations. Finally, we implement the computational codes in Matlab software and perform the comparison between theory and simulations.
