This article discusses numerical analysis of the distributed optimal control problem governed by the von K\'{a}rm\'{a}n equations defined on a polygonal domain in $\mathbb{R}^2$. The state and adjoint variables are discretised using the nonconforming Morley finite element method and the control is discretized using piecewise constant functions. A priori and a posteriori error estimates are derived for the state, adjoint and control variables. The a posteriori error estimates are shown to be efficient. Numerical results that confirm the theoretical estimates are presented.

翻译：本篇文章讨论由 von K\'{a}rm\'{a}n 等式($\mathb{R}2$)定义的多边形域定义的分布式最佳控制问题的数字分析。 状态变量和连接变量使用不兼容的 Morley 有限元素法分解, 控制则使用片状常数函数分解。 为状态变量、连接变量和控制变量得出先验和后验错误估计数。 后验错误估计数显示为有效。 提供了证实理论估计数的数字结果 。