FINITE-ELEMENT SCHEMES FOR NONLINEAR PROBLEMS IN INFINITE DOMAINS

A class of non-linear elliptic problems in infinite domains is conside red, with non-linearities extending to infinity. Examples include stea dy-state heat radiation from an infinite plate, and the deflection of an infinite membrane on a non-linear elastic foundation. Also, this cl ass of problems may serve as a starting point for treating non-linear wave problems. The Dirichlet-to-Neumann (DtN) Finite Element Method, w hich was originally developed for linear problems in infinite domains, is extended here to solve these non-linear problems. Several DtN sche mes are proposed, with a trade-off between accuracy and computational effort. Numerical experiments which demonstrate the performance of the se schemes are presented. (C) 1998 John Wiley & Sons, Ltd.