Finite element schemes for nonlinear problems in infinite domains. (English) Zbl 0907.73061
Summary: A class of nonlinear elliptic problems in infinite domains is considered, with nonlinearities extending to infinity. Examples include steady-state heat radiation from an infinite plate, and the deflection of an infinite membrane on a nonlinear elastic foundation. Also, this class of problems may serve as a starting point for treating nonlinear 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 nonlinear 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K20 | Plates |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
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