We develop a method to compute the $H^2$-conforming finite element approximation to planar fourth order elliptic problems without having to implement $C^1$ elements. The algorithm consists of replacing the original $H^2$-conforming scheme with pre-processing and post-processing steps that require only an $H^1$-conforming Poisson type solve and an inner Stokes-like problem that again only requires at most $H^1$-conformity. We then demonstrate the method applied to the Morgan-Scott elements with three numerical examples.

翻译：我们提出了一种方法，用于计算平面四阶椭圆问题的$H^2$相容有限元近似，而无需实现$C^1$单元。该算法通过预处理和后处理步骤替代原始的$H^2$相容格式，仅需一个$H^1$相容的泊松型求解，以及一个内部的类斯托克斯问题，后者同样仅需至多$H^1$相容性。随后，我们通过三个数值示例展示了该方法在Morgan-Scott单元上的应用。