A Nitsche-based method for unilateral contact problems: numerical analysis

Abstract : We 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 satisfied.
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SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2013, 51 (2), p. 1295-1307. 〈10.1137/12088344X〉
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Franz Chouly, Patrick Hild. A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2013, 51 (2), p. 1295-1307. 〈10.1137/12088344X〉. 〈hal-00717711〉

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