The condition for constructing a finite element from a superspline

Document detail

ID

oai:arXiv.org:2407.03680

Topic

Mathematics - Numerical Analysis 65N30, 65D07

Author

Hu, Jun Lin, Ting Wu, Qingyu Yuan, Beihui

Year

2024

listing date

7/10/2024

Keywords

spaces element superspline finite

Metrics

Abstract

This paper addresses the sufficient and necessary conditions for constructing $C^r$ conforming finite element spaces from a superspline spaces on general simplicial triangulations.

We introduce the concept of extendability for the pre-element spaces, which encompasses both the superspline space and the finite element space.

By examining the extendability condition for both types of spaces, we provide an answer to the conditions regarding the construction.

A corollary of our results is that constructing $C^r$ conforming elements in $d$ dimensions should in general require an extra $C^{2^{s}r}$ continuity on $s$-codimensional simplices, and the polynomial degree is at least $(2^d r + 1)$.

;Comment: 22 pages, 4 figures

Hu, Jun,Lin, Ting,Wu, Qingyu,Yuan, Beihui, 2024, The condition for constructing a finite element from a superspline