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Galerkin least squares finite element method for the obstacle problem
Department of Mathematics, University College London.
Jönköping University, School of Engineering, JTH, Product Development. Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University.
Department of Mathematics and Systems Analysis, Aalto University.
2017 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 313, 362-374 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 313, 362-374 p.
Keyword [en]
Obstacle problem, Augmented Lagrangian method, A priori error estimate, A posteriori error estimate, Adaptive method
National Category
Applied Mechanics Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-32063DOI: 10.1016/j.cma.2016.09.025ISI: 000390740900016ScopusID: 2-s2.0-84994018818Local ID: JTHproduktutvecklingISOAI: oai:DiVA.org:hj-32063DiVA: diva2:1040311
Available from: 2016-10-27 Created: 2016-10-27 Last updated: 2017-01-20Bibliographically approved

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Citation style
  • apa
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  • vancouver
  • Other style
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  • de-DE
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  • Other locale
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Output format
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