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Finite element schemes for non‐linear problems in infinite domains
Author(s) -
Givoli Dan,
Patlashenko Igor
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980530)42:2<341::aid-nme371>3.0.co;2-5
Subject(s) - finite element method , mathematics , class (philosophy) , linear elasticity , dirichlet distribution , infinity , nonlinear system , mathematical analysis , computer science , boundary value problem , engineering , physics , structural engineering , quantum mechanics , artificial intelligence
A class of non‐linear elliptic problems in infinite domains is considered, with non‐linearities extending to infinity. Examples include steady‐state heat radiation from an infinite plate, and the deflection of an infinite 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 originally developed for linear problems in infinite domains, is extended here to solve these non‐linear problems. Several DtN schemes are proposed, with a trade‐off between accuracy and computational effort. Numerical experiments which demonstrate the performance of these schemes are presented. © 1998 John Wiley & Sons, Ltd.