Computing [math]-Conforming Finite Element Approximations Without Having to Implement [math]-Elements

Abstract

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page A2398-A2420, August 2024.
Abstract. We develop a method to compute the [math]-conforming finite element approximation to planar fourth order elliptic problems without having to implement [math] elements. The algorithm consists of replacing the original [math]-conforming scheme with preprocessing and postprocessing steps that require only an [math]-conforming Poisson type solve and an inner Stokes-like problem that again only requires at most [math]-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.