The Uncoupling of Boundary Integral and Finite Element Methods for Nonlinear Boundary Value Problems

In this paper the uncoupling of boundary integral and finite element methods is applied to study the weak solvability of certain nonlinear exterior boundary value problems. As a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane, which becomes the Laplace equation in the corresponding unbounded exterior region. We provide sufficient conditions for the nonlinear coefficients from which existence, uniqueness, and approximation results are established. In particular, nonlinear equations yielding both monotone and nonmonotone operators are analyzed.