Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements
Numerical Analysis
2024-06-04 v1 Numerical Analysis
Abstract
We develop a method to compute -conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational formulation involving spaces with at most -smoothness, so that conforming discretizations require at most -continuity. The method is demonstrated on arbitrary order -splines.
Cite
@article{arxiv.2406.00338,
title = {Two and three dimensional $H^2$-conforming finite element approximations without $C^1$-elements},
author = {Mark Ainsworth and Charles Parker},
journal= {arXiv preprint arXiv:2406.00338},
year = {2024}
}