FEM and BEM coupling for a nonlinear transmission problem with Signorini contact

This paper is concerned with the interface problem consisting of a nonlinear uniformly monotone partial differential equation in some bounded Lipschitz domain Omega in R-n (n = 2 or n greater than or equal to 3) and the Laplace equation with some radiation condition in the unbounded exterior domain Omega(c):= R-n\<(Omega)over bar>. The two problems are coupled by transmission conditions and Signorini contact conditions on the interface Gamma = partial derivative Omega. The exterior part of the interface problem is rewritten in terms of boundary integral operators. This leads to a variational inequality with a nonlinear monotone operator. By this approach, existence and uniqueness of a solution in appropriate Sobolev spaces are obtained. Its approximation is performed by coupling the finite element method (FEM) (in Omega) and the boundary element method (BEM) (the latter living on the interface Gamma), yielding a discrete monotone variational inequality. We present an abstract Cea-type error estimate and derive asymptotic error estimates.