Burman, E;
Hansbo, P;
Larson, M;
(2019)
Augmented Lagrangian finite element methods for contact problems.
ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)
, 53
(1)
pp. 173-195.
10.1051/m2an/2018047.
Preview |
Text
Burman_final_plain.pdf - Accepted Version Download (2MB) | Preview |
Abstract
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.
| Type: | Article |
|---|---|
| Title: | Augmented Lagrangian finite element methods for contact problems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an/2018047 |
| Publisher version: | https://doi.org/10.1051/m2an/2018047 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | math.NA, math.NA, 65M60, 65M12, 74M15 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1518357 |
Archive Staff Only
 |
View Item |
