Emergent Mind
Computing $H^2$-conforming finite element approximations without having to implement $C^1$-elements
(2311.04771)
Published Nov 8, 2023
in
math.NA
and
cs.NA
Abstract
We develop a method to compute the $H2$-conforming finite element approximation to planar fourth order elliptic problems without having to implement $C1$ elements. The algorithm consists of replacing the original $H2$-conforming scheme with pre-processing and post-processing steps that require only an $H1$-conforming Poisson type solve and an inner Stokes-like problem that again only requires at most $H1$-conformity. We then demonstrate the method applied to the Morgan-Scott elements with three numerical examples.
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