Computing $H^2$-conforming finite element approximations without having to implement $C^1$-elements
- Resource Type
- Working Paper
- Authors
- Ainsworth, Mark; Parker, Charles
- Source
- Subject
- Mathematics - Numerical Analysis
65N30, 65N12
- Language
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.
Comment: 23 pages, 8 figures