English

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 H2H^2-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 H1H^1-smoothness, so that conforming discretizations require at most C0C^0-continuity. The method is demonstrated on arbitrary order C1C^1-splines.

Keywords

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}
}
R2 v1 2026-06-28T16:49:26.388Z