Burman, E;
Hansbo, P;
Larson, MG;
Stenberg, R;
(2017)
Galerkin least squares finite element method for the obstacle problem.
Computer Methods in Applied Mechanics and Engineering
, 313
pp. 362-374.
10.1016/j.cma.2016.09.025.
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Abstract
We construct a consistent multiplier free method for the finite element solution of the obstacle problem. The method is based on an augmented Lagrangian formulation in which we eliminate the multiplier by use of its definition in a discrete setting. We prove existence and uniqueness of discrete solutions and optimal order a priori error estimates for smooth exact solutions. Using a saturation assumption we also prove an a posteriori error estimate. Numerical examples show the performance of the method and of an adaptive algorithm for the control of the discretization error.
| Type: | Article |
|---|---|
| Title: | Galerkin least squares finite element method for the obstacle problem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.cma.2016.09.025 |
| Publisher version: | http://dx.doi.org/10.1016/j.cma.2016.09.025 |
| Language: | English |
| Additional information: | © 2016 Elsevier. This manuscript version is made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at https://creativecommons.org/licenses/. Access may be initially restricted by the publisher. |
| Keywords: | Obstacle problem; Augmented Lagrangian method; A priori error estimate; A posteriori error estimate; Adaptive method |
| UCL classification: | UCL 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/1517995 |
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