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
26.03.2025
Schlüsselwörter
spaces finite superspline elementZusammenfassung
This paper addresses sharpness 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 spaces and the finite element spaces.
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 generally requires an extra $C^{2^{s}r}$ continuity on $s$-codimensional simplices, and the polynomial degree is at least $(2^d r + 1)$.
;Comment: 21 pages, 4 figures
Hu, Jun,Lin, Ting,Wu, Qingyu,Yuan, Beihui, 2024, The sharpness condition for constructing a finite element from a superspline
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