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 m ethods is applied to study the weak solvability of certain nonlinear e xterior boundary value problems. As a model we consider a nonlinear se cond order elliptic equation in divergence form in a bounded inner reg ion of the plane, which becomes the Laplace equation in the correspond ing unbounded exterior region. We provide sufficient conditions for th e nonlinear coefficients from which existence, uniqueness, and approxi mation results are established. In particular, nonlinear equations yie lding both monotone and nonmonotone operators are analyzed. (C) 1995 A cademic Press. Inc.