Computing \(H²\)-Conforming Finite Element Approximations Without Having to Implement \(C¹\)-Elements

We develop a method to compute the [Formula: see text]-conforming finite element approximation to planar fourth order elliptic problems without having to implement [Formula: see text] elements. The algorithm consists of replacing the original [Formula: see text]-conforming scheme with preprocessing and postprocessing steps that require only an [Formula: see text]-conforming Poisson type solve and an inner Stokes-like problem that again only requires at most [Formula: see text]-conformity. We then demonstrate the method applied to the Morgan–Scott elements with three numerical examples. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://doi.org/10.5281/zenodo.10070565 . [Formula: see text]