Dokumentdetails
ID
oai:arXiv.org:2407.03680
Thema
Mathematics - Numerical Analysis 65N30, 65D07Autor
Hu, Jun Lin, Ting Wu, Qingyu Yuan, BeihuiKategorie
Computer Science
Jahr
2024
Auflistungsdatum
10.07.2024
Schlüsselwörter
spaces element superspline finiteZusammenfassung
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
