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Augmented Lagrangian finite element methods for contact problems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
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
2019. Vol. 53, no 1, p. 173-195
Keywords [en]
Signorini problem, obstacle problem, finite element method, Lagrange mutlipliers, augmented grangian, error estimates
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-158369DOI: 10.1051/m2an/2018047ISI: 000464277200001OAI: oai:DiVA.org:umu-158369DiVA, id: diva2:1307295
Funder
Swedish Research Council, 2011-4992Swedish Research Council, 2013-4708Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-04-26Bibliographically approved

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Larson, Mats G.

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