Schwarz method for dual contact problems

Lori Badea (1) , Frédéric Lebon (2)

1 IMAR - "Simion Stoilow" Institute of Mathematics
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

In this paper, we analyze the convergence of the Schwarz method for contact problems with Tresca friction formulated in stress variables. In this dual variable, the problem is written as a variational inequality in the space $H_\text{div}(\Omega)$, $\Omega$ being the domain of the problem. The method is introduced as a subspace correction algorithm. In this case, the global convergence and the error estimation of the method are already proved in the literature under some assumptions. However, the checking of these hypotheses in the space $H_\text{div}(\Omega)$ cannot be proved easily, as for the space $H^1(\Omega)$. The main result of this paper is to prove that these hypotheses are verified for this particular variational inequality. As in the case of the classical problems formulated in primal variables, the error estimate we obtain depends on the overlapping parameter of the domain decomposition.

Mots clés: Variational inequalities; Domain decomposition methods; Dual formulation; Contact problems; Schwarz method; Subspace correction methods

Domaines: Mécanique des solides [physics.class-ph]

Lori Badea, Frédéric Lebon. Schwarz method for dual contact problems. Computational & Applied Mathematics, 2017, 36 (1), pp.719-731. ⟨10.1007/s40314-015-0255-y⟩. ⟨hal-01508775⟩