Volume 57, Number 3, May-June 2023
|Page(s)||1731 - 1746|
|Published online||26 May 2023|
A Nitsche method for the elastoplastic torsion problem
Université de Bourgogne, Institut de Mathématiques de Bourgogne, 21078 Dijon, France
2 Center for Mathematical Modeling and Department of Mathematical Engineering, University of Chile and IRL 2807 – CNRS, Santiago, Chile
3 Departamento de Ingeniería Matemática, CI 2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile
4 Institut de Mathématiques de Toulouse – UMR CNRS 5219, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
5 Department of Mathematics and Systems Analysis, Aalto University, Otakaari 1 F, Espoo, Finland
* Corresponding author: email@example.com
Accepted: 20 April 2023
This study is concerned with the elastoplastic torsion problem, in dimension n ≥ 1, and in a polytopal, convex or not, domain. In the physically relevant case where the source term is a constant, this problem can be reformulated using the distance function to the boundary. We combine the aforementioned reformulation with a Nitsche-type discretization as in Burman et al. [Comput. Methods Appl. Mech. Eng. 313 (2017) 362–374]. This has two advantages: (1) it leads to optimal error bounds in the natural norm, even for nonconvex domains; (2) it is easy to implement within most of finite element libraries. We establish the well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments.
Mathematics Subject Classification: 65N15 / 65N30 / 74C05
Key words: Variational inequalities / elastoplastic torsion problem / finite elements / Nitsche / error estimates
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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