A Posteriori Estimates for a Natural Neumann–Neumann Domain Decomposition Algorithm on a Unilateral Contact Problem

D. Choi 1 L. Gallimard 2 T. Sassi 1
1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 LEME - Laboratoire Energétique Mécanique Electromagnétisme
Abstract : In this paper we present an error estimator for unilateral contact problems solved by a Neumann–Neumann Domain Decomposition algorithm. This error estimator takes into account both the spatial error due to the finite element discretization and the algebraic error due to the domain decomposition algorithm. To differentiate specifically the contribution of these two error sources to the global error, two quantities are introduced: a discretization error indicator and an algebraic error indicator. The effectivity indices and the convergence of both the global error estimator and the error indicators are shown on several examples.
Keywords : Error estimation Domain decomposition algorithm Contact problem Discretization error Algebraic error
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D. Choi, L. Gallimard, T. Sassi. A Posteriori Estimates for a Natural Neumann–Neumann Domain Decomposition Algorithm on a Unilateral Contact Problem. Journal of Scientific Computing, Springer Verlag, 2015, 64 (3), pp.818 - 836. ⟨10.1007/s10915-014-9944-8⟩. ⟨hal-01690027⟩

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