Computing H²-conforming finite element approximations without having to implement C¹-elements

2023/11/08 by Ainsworth, Mark, Parker, Charles
#65N12 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2311.04771

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.

Related

• Two and three dimensional H²-conforming finite element approximations without C¹-elements
• An H²(curl)-conforming finite element in 2D and its applications to the quad-curl problem
• Analysis of a combined NC1-C2 method for elliptic problem
• Stable C¹-conforming finite element methods for a class of nonlinear fourth-order evolution equations
• A construction of canonical nonconforming finite element spaces for elliptic equations of any order in any dimension