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Augmented Lagrangian finite element methods for contact problems
Department of Mathematics, University College London, United Kingdom.
Jönköping University, School of Engineering, JTH, Materials and Manufacturing.ORCID iD: 0000-0001-7352-1550
Department of Mathematics and Mathematical Statistics, Umeå University, Sweden.
2019 (English)In: Mathematical Modelling and Numerical Analysis, ISSN 0764-583X, E-ISSN 1290-3841, Vol. 53, no 1, p. 173-195Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
EDP Sciences, 2019. Vol. 53, no 1, p. 173-195
Keywords [en]
Augmented Lagrangian, Error estimates, Finite element method, Lagrange mutlipliers, Obstacle problem, Signorini problem, Constrained optimization, Augmented Lagrangians, Lagrange, Obstacle problems, Lagrange multipliers
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hj:diva-43538DOI: 10.1051/m2an/2018047ISI: 000464277200001Scopus ID: 2-s2.0-85064252246Local ID: ;JTHMaterialISOAI: oai:DiVA.org:hj-43538DiVA, id: diva2:1307094
Available from: 2019-04-25 Created: 2019-04-25 Last updated: 2019-04-25Bibliographically approved

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Hansbo, Peter

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