Mixed FEM and the discontinuous Petrov-Galerkin (DPG) methodology in numerical homogenization
Authors:
- Marta Oleksy,
- Witold Cecot
Abstract
The mixed finite element method uses an approximation of at least two fields (e.g. displacements and stresses). Even though it is difficult to construct stable approximation for such formulations, the mixed methods provide much better convergence of the flux than the standard methods, even for heterogeneous materials with a high contrast of component parameters. Furthermore, the mixed formulations are well-posed for incompressible materials. In this work a novel application of the mixed FEM to computational homogenization is presented and examined. Conformity with the H(div) space is provided by the Piola transformation and the approximation orders are assumed according to the exact sequence of energy spaces. The modified Hellinger-Reissner principle with weakly imposed stress tensor symmetry through the introduction of the Lagrange multiplier is used and the Discontinuous Petrov-Galerkin approach (DPG), with built-in a posteriori error estimation, provides stability of approximation.
- Record ID
- CUT158f9a415127484b9a33ce0ca5d5b44d
- Publication categories
- ; ;
- Author
- Pages
- [1-14]
- Other elements of collation
- rys.; tab.; wykr.; Bibliografia (na s.) - 13-14; Bibliografia (liczba pozycji) - 18; Oznaczenie streszczenia - Abstr.
- Book
- Cecot Witold, Witold Cecot Kozień Marek, Marek Kozień Lisowski Wojciech Wojciech Lisowski [et al.] (eds.): 4th Polish Congress of Mechanics and the 23rd International Conference on Computer Methods in Mechanics, AIP Conference Proceedings, no. 2239, 2020, [Melville], American Institute of Physics, AIP Publishing, ISBN 978-0-7354-1998-8
- Keywords in English
- mixed FEM, DPG, homogenization
- DOI
- DOI:10.1063/5.0007806 Opening in a new tab
- URL
- https://aip.scitation.org/doi/abs/10.1063/5.0007806 Opening in a new tab
- Related project
- Połączenie wieloskalowej metody elementów skończonych z nieciągłym podejściem Petrowa-Galerkina. . Project leader at PK: , ,
Projects financed by NSC [Projekty finansowane przez NCN] - Language
- eng (en) English
- License
- Score (nominal)
- 20
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT158f9a415127484b9a33ce0ca5d5b44d/
- URN
urn:pkr-prod:CUT158f9a415127484b9a33ce0ca5d5b44d
* 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.