Finite element schemes for non-linear problems in infinite domains

A class of non-linear elliptic problems in in nite domains is considered, with non-linearities extending to in nity. Examples include steady-state heat radiation from an in nite plate, and the de ection of an in nite membrane on a non-linear elastic foundation. Also, this class of problems may serve as a starting point for treating non-linear wave problems. The Dirichlet-to-Neumann (DtN) Finite Element Method, which was orig- inally developed for linear problems in in nite domains, is extended here to solve these non-linear problems. Several DtN schemes are proposed, with a trade-o between accuracy and computational e ort. Numerical experiments which demonstrate the performance of these schemes are presented.