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Galerkin least squares finite element method for the obstacle problem

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. Green open access

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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 > School of BEAMS
UCL > School of BEAMS > Faculty of Maths and Physical Sciences
URI: http://discovery.ucl.ac.uk/id/eprint/1517995
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