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Reduction methods for nonlinear steady-state thermal analysis. (English) Zbl 0557.65076

A numerical technique to deal with nonlinearities in steady-state problems is considered, that was developed earlier for structural analysis problems by the first author [Comput. Struct. 13, 31-44 (1981; Zbl 0455.73080)]. This method is applied to four different problems to determine temperature fields in one- and two-dimensional domains. The methods uses a perturbation technique by introducing one or more parameters into the governing equation. This is combined with the Galerkin approach to reduce the number of free parameters. The accuracy of the solutions obtained is shown by numerical experiments.
Reviewer: U.Hornung

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
74A15 Thermodynamics in solid mechanics

Citations:

Zbl 0455.73080
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References:

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