A Nitsche-Based Method for Unilateral Contact Problems: Numerical Analysis
- 1 January 2013
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 51 (2), 1295-1307
- https://doi.org/10.1137/12088344x
Abstract
International audienceWe introduce a Nitsche-based formulation for the finite element discretization of the unilateral contact problem in linear elasticity. It features a weak treatment of the non-linear contact conditions through a consistent penalty term. Without any additional assumption on the contact set, we can prove theoretically its fully optimal convergence rate in the H1(Ω)-norm for linear finite elements in two dimensions, which is O(h^(1/2+ν)) when the solution lies in H^(3/2+ν)(Ω), 0 < ν ≤ 1/2. An interest of the formulation is that, conversely to Lagrange multiplier-based methods, no other unknown is introduced and no discrete inf-sup condition needs to be satisfiedKeywords
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