On pressure robustness and independent determination of displacement and pressure in incompressible linear elasticity
Authors:
- Adam Zdunek,
- Michael Neunteufel,
- Waldemar Rachowicz
Abstract
We investigate the possibility to determine the divergence-free displacement u independently from the pressure reaction p for a class of boundary-value problems in incompressible linear elasticity. If not possible, we investigate if it is possible to determine it pressure robustly, i.e. pollution free from the pressure reaction. For convex domains there is but one variational boundary value problem among the investigated that allows the independent determination. It is the one with essential no-penetration conditions combined with homogeneous tangential traction conditions. Further, for the investigated cases, the weakly divergence-free displacement can be computed pressure robustly provided the total body force is decomposed into its direct sum of divergence- and rotation-free components using the Helmholtz decomposition. The elasticity problem is solved using these components as separate right-hand sides. The total solution is obtained using the superposition principle. We employ a (u, p) higher-order finite element formulation with discontinuous pressure elements. It is inf–sup stable for polynomial degree p ≥ 2 but not pressure robust by itself. We propose a three step procedure to solve the elasticity problem which includes by the Helmholtz decomposition of the total body force. The extra cost for the three-step procedure is essentially the cost for the Helmholtz decomposition of the assembled total body force, and the small cost of solving the elasticity problem with one extra right-hand side. The results are corroborated by theoretical derivations as well as numerical results.
- Record ID
- CUT1fcf76ca840d4d0887437853ec9c414c
- Publication categories
- ;
- Author
- Journal series
- Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, e-ISSN 1879-2138
- Issue year
- 2023
- Vol
- 403
- No
- Pt. A
- Pages
- [1-34]
- Article number
- 115714
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 33-34; Bibliografia (liczba pozycji) - 32; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 403, Pt. A
- Keywords in English
- incompressible, isotropic, linear elasticity, finite element, pressure robust
- ASJC Classification
- ; ; ; ;
- DOI
- DOI:10.1016/j.cma.2022.115714 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S0045782522006697 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 200
- Score source
- journalList
- Score
- Publication indicators
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT1fcf76ca840d4d0887437853ec9c414c/
- URN
urn:pkr-prod:CUT1fcf76ca840d4d0887437853ec9c414c
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.