This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise \(H^1\) and \(L^2\) norms are also derived. A working procedure to find an approximation for the discrete solution using Newton’s method is discussed. Numerical results that justify theoretical estimates are presented.

中文翻译：

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冯卡门方程的莫利型虚元法

本文分析了非相容 Morley 型虚拟单元方法，以近似描述极薄弹性板弯曲的 von Kármán 方程的正则解。讨论了非线性问题离散解的局部存在性和唯一性。能量范数中的先验误差估计是在精确解的最小规律性假设下建立的。还导出了分段\(H^1\)和\(L^2\)范数中的误差估计。讨论了使用牛顿法寻找离散解的近似值的工作过程。给出了证明理论估计合理性的数值结果。