0562017 - MÚ 2023 RIV DE eng J - Journal Article
Korotov, S. - Křížek, Michal - Kučera, V.
On degenerating finite element tetrahedral partitions.
Numerische Mathematik. Roč. 152, č. 2 (2022), s. 307-329. ISSN 0029-599X. E-ISSN 0945-3245
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : finite element * tetrahedral partitions
OECD category: Pure mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00211-022-01317-9

Degenerating tetrahedral partitions show up quite often in modern finite element analysis. Actually the commonly used maximum angle condition allows some types of element degeneracies. Also, mesh generators and various adaptive procedures may easily produce degenerating mesh elements. Finally, complicated forms of computational domains (e.g. along with a priori known solution layers, etc) may demand the usage of elements of various degenerating shapes. In this paper, we show that the maximum angle condition presents a threshold property in interpolation theory, as the interpolation error may grow (or at least does not decay) if this condition is violated (which does not necessarily imply that FEM error grows). We also demonstrate that the popular red refinements, if done inappropriately, may lead to degenerating partitions which break the maximum angle condition. Finally, we prove that not all tetrahedral elements from a family of tetrahedral partitions are badly shaped when the discretization parameter tends to zero.
Permanent Link: https://hdl.handle.net/11104/0334444