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Nonlinear heat conduction in composite bodies: A boundary element formulation. (English) Zbl 0633.65117
The paper discusses the numerical solution of the steady state nonlinear heat conduction problem by the boundary element method. Temperature- dependent conductivities are treated by the Kirchhoff transformation. The resulting nonlinear boundary conditions and also those of radiative type are approximated using piecewise constant boundary elements giving rise to a system of nonlinear equations which are solved by a modified Newton- Raphson method. In numerical examples the method compares favourably with finite elements.
Reviewer: J.D.P.Donnelly

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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